1. For Summer BTs, Posted throughout May & June 2016

   REMINDER: Answers in red.  Solvers (submitted) in blue. (Forgive any omissions.) Comments in green. For further elaboration, feel free to ask! 

   1. A palindrome is a number, like 535, that reads the same forward or backward.  How many palindromes are there between 10 & 1000? 99.  Jim Waterman, Dan Felsin, Anita Dixon, Amy Ragsdale, Rita Barger, Jennifer Vise.

2. A cheetah was clocked running 550 feet in 10 seconds.  How many miles per hour is that? 37.5 mph. Dan Felsin, Anita Dixon, Amy Ragsdale, Rita Barger.
3. The sum of A & B is 112.  If A is 4 more than C, and B is 2 less than C, what does C equal? 55.  Dan Felsin, Anita Dixon, Amy Ragsdale, Rita Barger, Jennifer Vise.
4. Name two consecutive prime numbers whose product is 899. 29 and 31. Anita Dixon, Amy Ragsdale, Rita Barger.
5. If you omit the digit common to both numerator and denominator of 26/65, you don’t change its value, because 26/65 = 2/5.  There are several fractions with that weird trait.  Can you find at least one more? (As always, a simple ‘yes’ or ‘no’ will not get full credit. :-)). There are SEVERAL more.  Just one example is 49/98 = 4/8. Jim Waterman, Anita Dixon, Rita Barger.  (JW has SEVERAL Comments here, if you haven’t seen them.)
6. Find the first place where there are three (3) consecutive integers which are all composite (not prime & not 0 or 1). 8, 9, 10. Jim Waterman, Anita Dixon, Amy Ragsdale, Rita Barger. [BONUS:  Can you do the same for 4?  5?  Any number?] Jim Waterman, Dan Felsin, Anita Dixon, Amy Ragsdale, Rita Barger, Jennifer Vise.  Some FASCINATING results here.  Also, RB noted some fascinating things I hadn’t quite thought of before!  (elaborations to appear one month in Math Tidbits)
7. Which of these is the biggest (largest in value) fraction?  3/7, 4/9, 2/5  4/9. Jim Waterman, Anita Dixon, Rita Barger.
8.  True or False:  A)  If the sum of two numbers is even, then both numbers are even.  B)  If the product of two numbers is even, then both numbers are even. C) A number with 5 factors is always bigger than another number with 4 factors.  All are false. Jim Waterman, Anita Dixon, Rita Barger, Jennifer Vise.
9. True or False:  I can’t seem to format the question parts in #8 so that they will number and indent correctly. In this particular case, the answer was true. And you can also imagine my frustration with the ill-formatted #1’s (twice!) above. Jim Waterman, Anita Dixon, Rita Barger, Jennifer Vise.
10. Every day from June 10 to June 19 this month was a palindrome!  (Reading the same front and back, disregarding punctuation – see also BT#1).  E.g. June 16:  6/16/16.  Cool!!  For this BT, A)  When did such a string last occur, if ever? 5/10/15 – 5/19/15. Anita Dixon, Rita Barger. B)  When will it next? 7/10/17 – 7/19/17. Anita Dixon, Rita Barger.
11. Alice won’t take part in the play if Betty is in it!  But Charles will only participate if Alice is in it.  The producer insists that one of the girls be in the play, and two people are needed total.  Who is in the play?  Alice and Charles. (Unless as JW noted, the director boots them both, keeps Betty, and casts a new person.  :-)). Jim Waterman, Anita Dixon, Rita Barger.
12. Find positive integers a, b, c such that 1/a + 1/b + 1/c = 1. a = 2, b = 3, c = 6.  (1/2 + 1/3 + 1/6 = 1).  ALSO, a = b = c = 3 will also work and is not ruled out. Jim Waterman, Anita Dixon, Rita Barger.
    

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For April BTs, Posted throughout April 2016

REMINDER: Answers in red.  Solvers (submitted) in blue.  For further elaboration, feel free to ask! (Please forgive any omissions – but notify me anyway.)

1. After a singularly dull lecture that followed a formal dinner, a man walked up to the lecturer and said, “Strikingly unoriginal.  I have a book that has every word of your speech in it, and most people here do, too.”  The lecturer was enraged and demanded proof.  He got it.  How?  The book was the dictionary.  Anita Dixon, Rita Barger, Amy Ragsdale, Bobbi Kneeshaw, Jennifer Vise.
2. A boy and a girl born on the same day of the same year with the same parents are not twins.  How is this possible? The boy and girl are part of a set of triplets (or quadruplets, . . .).  Anita Dixon, Rita Barger, Bobbi Kneeshaw.
3. A given cube has each side doubled to form a new cube.  How does the VOLUME of the new cube relate to the old one?  The volume of the new cube is 8 times that of the old one.  Anita Dixon, Rita Barger, Amy Ragsdale. 
4.  In BT #3 above, how is the surface area of the new cube changed?  (This is what some submitters thought I meant above.) The surface area of the new cube is 4 times that of the old one.  Anita Dixon, Rita Barger, Amy Ragsdale.

NOTE the possible ‘real world’ application arising from #3 & #4.  E.g., Say you’re a manufacturer seeking efficient sizes for your shipping boxes.  If your boxes are cubes and you double the edge of all sides, you can hold 8 times the material for only four times the cardboard costs. 

5.  You have four colored chips – 2 black, 1 yellow, and 1 white.  The are in a horizontal line, left to right.  The white chip is directly to the left of a black chip, and neither black chip is on an end.  How are the colored chips aligned?  W, B, B, Y.   Anita Dixon, Rita Barger, Amy Ragsdale, Bobbi Kneeshaw, Jennifer Vise.
6.  See #5.  Same set-up, but the chips are now 2 red, 1 yellow, and 1 green.  The yellow chip is not on an end, and the two ends are different colors.  The red chips are not adjacent, and the green chip is on the far right.  How are the chips aligned now?  R, Y, R, G.  Anita Dixon, Rita Barger, Amy Ragsdale, Bobbi Kneeshaw, Jennifer Vise.
7.  This mailing was sent out on 4/25/16.  This is a ‘triple square’ day, as all three entries are perfect squares.   a)  How many triple square days occur this year? 15 (5 days in each of Jan, Apr, and Sept).  b)  How many of these have all 3 numbers different?  9  c)  Before 2016, when was the last triple square day? 9/25/09. (The last time all 3 were different squares was 4/25/09, over 5 years ago.)  NOTE:  I didn’t ask, but after 9/25/16, the next triple square day doesn’t occur until 1/1/25.  Anita Dixon, Rita Barger, Amy Ragsdale, Bobbi Kneeshaw all got all parts.

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For March BTs, Posted throughout March 2016

REMINDER: Answers in red.  Solvers (submitted) in blue.  For further elaboration, feel free to ask! (Please forgive any omissions – but notify me anyway.)

1. Judo and karate contests take place on square mats.  The karate mat is 8 meters on a side, while the judo mat has 4 times the area of the karate mat.  What is the length of each side of a judo mat?  16 meters.  Rita Barger, Amy Ragsdale, Jennifer Vise.
2. Using the digits 1 – 6 once each, what is the largest proper+ fraction (less than 1) that you can form? (E.g. 234/516 is bigger than 1/3, but one can do better.)  463/512 is over 9/10, and is the biggest.  NOTE:  This one surprised me.  Upon first glance, I was sure it would be 5-something/6-something, but the earlier one is slightly better.  Rita Barger, Amy Ragsdale.
3.  Jack had a bag of 128 apples.  He sold 25 percent of them to Jill.  Next he sold 25 percent of those remaining to June.  Finally, he gave the shiniest one of those remaining to his teacher.  After that, how many did he have? 71 apples. Rita Barger, Amy Ragsdale, Jim Waterman, Jennifer Vise.
4.  I have twice as many nickels as dimes.  If the value of my nickels is $5.00, what is the value of my dimes? $5, also. Rita Barger, Amy Ragsdale, Jim Waterman, Jennifer Vise.
5.  What do shredded wheat, aspirin, zipper, yo-yo, and cellophane have in common? (Possibly more than one answer?) One answer:  They all started out as brand name items, which later became generic names for the general concept.  No one produced that answer, but Rita Barger gave several other creative ones, and Jim Waterman produced his ‘usual’ wild one:  “All were used in a sentence by Larry Campbell.”
6. Given an 8×8 checker/chess board, how many squares of any size (not just 1 x 1) are there? 204 (64 + 49 + 36 + 25 + 16 + 9 + 4 + 1). Rita Barger, Jennifer Vise.
7. There is a pole in a pond. One-half of the pole is in the ground (under the pond), another one-third of it is covered by water, and 8 ft is out of the water. What is the total length of the pole in ft, and how deep is the pond at that point?  48 feet (pole) and 16 feet (pond). Rita Barger, Amy Ragsdale.
8. My neighbor has four daughters and each daughter has a brother.  How many children does my neighbor have? 5 – 4 girls and 1 boy. Rita Barger, Amy Ragsdale, and Jennifer Vise.
   

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For February BTs, Posted throughout February 2016

REMINDER: Answers in red.  Solvers (submitted) in blue.  For further elaboration, feel free to ask!

1. What can you hold in your left hand, but not your right hand? (Multiple answers?)  Right arm, wrist, elbow, etc.  Rita Barger, Jennifer Vise, Amy Ragsdale.
2.  In the US, 5/2 means May 2, but in England it means Feb 5 (they put the day first).  How many days each year have the same abbreviations in both countries?  Twelve (12).  1/1, 2/2, etc.   Rita Barger, Amy Ragsdale, Jim Waterman.
3. What is the next combination of letters and numbers in this pattern?  A1Z26, B3Y24, C5X22, D7W20. Rita Barger, Jennifer Vise, Amy Ragsdale, Jim Waterman.
4. Find the smallest of 5 consecutive integers whose sum is 100.  18.  (18 + . . . +22 = 100). Rita Barger, Jennifer Vise, Amy Ragsdale, Jim Waterman.
5. Find any value of t that makes 19/t + 5/t a whole number.  (Mini Bonus:  Can you find all values of t that work?)  Using any of 1,2,3,4,6,8,12, or 24 for t will work.  (In general, any divisor of 24.)  Rita Barger, Jennifer Vise, Amy Ragsdale, Jim Waterman.
6. At what time is the sum of the digits on a digital clock the greatest?  9:59  Rita Barger, Jennifer Vise, Jim Waterman.
7. The transistor was invented in a year close to the middle of the 20^th century. The tens’ digit of the year is 4 times the thousands’ digit and one-half of the ones’ digit.  In what year was it invented?  1948.  Rita Barger, Jennifer Vise, Jim Waterman.
8. Two 5 x 5 squares overlap to form a 5 x 7 rectangle. What is the area of the region in which the two squares overlap? 15 square units. (The overlap is 3 x 5).  Rita Barger, Jim Waterman.
9. What fraction of the small squares on a chessboard are covered (occupied) by playing pieces at the start of the game?  One half.  (32 of the 64).  Rita Barger, Jennifer Vise, Jim Waterman.
10. Eric’s school system has 9000 pupils and a teacher-pupil ratio of 1:30. They feel this is too high, and want to reduce it to 1:25.  How many more or fewer teachers are needed to achieve this goal?  A 1:30 ratio requires 300 teachers.  A 1:25 ratio requires 360 teachers.  So 60 teachers would need to be hired. Rita Barger, Jim Waterman.

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For January BTs, Posted throughout January 2016

REMINDER: Answers in red.  Solvers (submitted) in blue.  For further elaboration, feel free to ask!

1.  Answer either or both:  If you could spend $1 a minute,  how long would it take you to spend $1,000,000? A little less than two years. (Note:  Yes, an answer of ‘one million minutes’ is technically correct, but . . .   🙂 ).  If you spent a $20 bill a minute, how long would it take to spend one billion dollars? Over 95 years!  Rita Barger, Jennifer Vise
2. A bottle of old brandy costs $45.  The brandy costs $40 more than the empty bottle.  What is the cost of the empty bottle? $2.50 (not $5, as is instinctual).  [Then brandy costs $42.50 – $40 more – and total is $45.]  Rita Barger, Amy Ragsdale.
3. James says “I have as many brothers as sisters.”  His sister says, “I have twice as many brothers as sisters.” How many brothers and sisters are in this family? Four brothers, three sisters.  Rita Barger, Jennifer Vise.
4. How many 3-digit numbers have all odd digits? 125 (5x5x5).  Rita Barger, Jennifer Vise, Amy Ragsdale.  Is the answer the same for all even digits?  NO.  There are only 100 of those (4x5x5 – no leading 0’s.)  Rita Barger, Amy Ragsdale.
5. Last month (see DecBT, #6), we encountered a problem where a piggy bank started with 2 cents in it and you doubled that amount each day.  At the end of ONE week, there was $1.28 in the bank.  If you were to continue that process (doubling the current amount with that day’s deposit), how much would be in the bank at the end of TWO weeks?  $327.68.  (Though Rita pointed out a possible reinterpretation, due to my vague statement, in which $1638.40 also works.)  Rita Barger.
6. Notice that 2 + 2 = 2 x 2.  Can you find three whole numbers whose sum also equals their product? 1, 2, 3.  1 + 2 + 3 = 1 x 2 x 3.  Rita Barger and Jim Waterman.   (Mini-Bonus:  If you’re allowed to use integers [negatives included], can you find three more?)  -1, 0, 1.  (Rita also pointed out that any triplet of the form -n, 0, n will also work.)  Rita Barger.
7. Suppose you have a 7-minute sand timer and an 11-minute sand timer.  What is the easiest way to time the boiling of an egg for 15 minutes? Start the 11-minute and 7-minute timers at the same time. When the 7 minute timer runs out, start boiling the egg. The 11-minute timer will have 4 minutes left in it. When it runs out, turn it over and start again. When it runs out the second time, the egg will have been boiling for 15 minutes. Rita Barger, Jim Waterman, Jennifer Vise, and Amy Ragsdale.
8. CONTEST? Using each of the 10 digits ONCE, find two different 5-digit numbers that have the largest product.  (Let’s also make this an ongoing contest – start somewhere and send in your best current answer whenever you have one, and we’ll keep track of the current record [and all submitters] weekly.  I’ll keep us posted.)  UPDATE 1:  Jim Waterman submits 97531 x 86420, which = 8,428,629,020, and is the CURRENT RECORD.  Thanks, Jim.  Final Note:  The two numbers 96,420 and 87,531 have a product of 8,439,739,020, which is slightly higher than Jim’s.  I suspect those are the two highest.
9. Jack is lighter than Phil, but heavier than Bob.  Bob is lighter than Jack, but heavier than Pete.  Which man is the heaviest, and which man is the lightest?  Phil is heaviest, Pete is lightest.  Rita Barger, Jim Waterman.
10. Gloria is making 97 SANDWICHES*  for a party.  How many packages OF SANDWICH ROLLS* does she need to buy, if the sandwich rolls come in pkgs of 8?  13 complete packages (with buns left over).  Rita Barger * So sorry for the missing words.  Thanks to Jim Waterman for noticing.
11. EXPLORATION/BONUS  Take a calculator and enter any six-digit number.  Hit the “square root” key until there is a ‘1’ before the decimal point.  How many times did it take?  Try it again (and again).  What do you find?  It always takes 5 times, no matter the size of the six-digit number.  Rita Barger (who also provided an explanation), Jennifer Vise.

12. BONUS 2  Do you remember the cartoon from Jan 4?  Check it out again here:  Explain how the 3rd logician knew that they all three wanted a beer.  (This is NOT as hard as these problems usually can be.  Give it a shot!)  Each of the first 2 knew they wanted a beer, so they couldn’t answer NO, and couldn’t answer YES, since neither knew about the 3rd person.  The 3rd person, realizing this, and knowing she too wanted a beer, could confidently answer YES.  Rita Barger, Jim Waterman

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Answers For December BTs, Posted in December 2015

REMINDER: Answers in red.  Solvers (submitted) in blue.  For further elaboration, feel free to ask!

1.  A milkman has 2 empty jugs: a 3 gallon jug and a 5 gallon jug.  How can he measure exactly 2 gallon without wasting any milk?  Fill the 3 gallon jug, empty it into the 5 gallon jug.  Then do it again.  The bigger jug will only hold 2 more gallons, leaving exactly one gallon in the smaller jug.  Rita Barger, Denise Griffen, Jennifer Vise.

2.  Alice came across a lion and a unicorn in a forest of forgetfulness. The lion lies every Monday, Tuesday and Wednesday and the other days he tells the truth.  The unicorn lies on Thursdays, Fridays and Saturdays and the other days of the week he speaks the truth.
On a given day, each beast said “Yesterday I was lying.”  Which day of the week was it? Thursday. (One could simply test each day of the week to see which one would work.)   Rita Barger, Denise Griffen.
3.  Mr. Brown has 6 black gloves and 6 brown gloves in his closet. He blindly picks up some gloves from the closet. What is the minimum number of gloves Mr. Brown will have to pick to be certain to find a pair of gloves of the same color? Three.  After the second pick, he will either have a match or one of each color.  Either way, he will have a match after the 3rd draw.  Rita Barger, Denise Griffen, Jennifer Vise.
4.  I visited a nearby park and watched the kids playing.  I saw that there were a total of 17 bicycles and tricycles. If the total number of wheels was 43, how many tricycles were there? Nine (and 8 bicycles).   Rita Barger, Denise Griffen, Jennifer Vise
5.  Man Wrinkle spent one-eighth of his life as a boy, one-fourth as a youth, and one-half as an active man. If Man Wrinkle spent 12 years as an old man, then how many years did he spend as an active man?  48 years.  (One can deduce that the last 12 years represent 1/8 of his life.)  Rita Barger.
6. A young boy gets a new piggy bank for Christmas. He puts one penny into it.  You decide to help.  You ALSO put in one penny and decide to double that amount each day for one week.  (You add 2 cents on Day 2, 4 cents on Day 3, etc.)  At the end of the week, how much money is in the bank?  $1.28  Rita Barger, Jennifer Vise.
7. Haretown and Tortoiseville are 81 miles apart. A hare travels at 7 miles per hour from Haretown to Tortoiseville, while a tortoise travels at 2 miles per hour from Tortoiseville to Haretown.If both set out toward each other at the same time, how many miles will the hare have to travel before meeting the tortoise en route?  Nine (9) hours. (One could use trial and error fairly quickly.)  Rita Barger, Jennifer Vise.   

 8.  A flagpole 9 feet high casts a shadow 3 feet long.  At that same time, how long a shadow would a 24-foot flagpole cast?  8 feet.  (The pole is three times as long as the shadow.)  Rita Barger.

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 *BONUS* A certain club has 10 members.  At their last meeting, each member was present, and each member shook hands with every other member.  How many total handshakes were there?

Forty-five (45).  (Several ways to deduce/figure this).  Rita Barger, Denise Griffen, Jennifer Vise

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Answers For November BTs, Posted throughout November 2015

REMINDER: Answers in red.  Solvers (submitted) in blue.  For further elaboration, feel free to ask!

Please forgive any oversights. Lots going on this month, and I was keeping track in various ways/places.

Posted 11/2/15:
1.  What 3 letters can be rearranged to form a beverage, a verb, or a homonym? (Is that term still used?) A, E, T.  (Tea, Eat, & Ate, among others?) Anita Dixon, Mike Brown, Rita Barger, Jim Waterman, Denise Griffin, Dave Krehbiel, Steve Kneeshaw.
2.  A plane crashes on the border of USA and Canada.  Where do they bury the survivors? Survivors are not usually buried. 🙂 Anita Dixon, Mike Brown, Rita Barger, Jim Waterman, Denise Griffin, Dave Krehbiel, Jennifer Vise, Christine Porter, Steve Kneeshaw.

Repeats from Nov ’14:  For newcomers and those with good memories.  🙂

3.  What are the next two letters in this sequence?  O, T, T, F, F, S, S, ___, ___  E, N.  (Eight, Nine). Anita Dixon, Mike Brown, Rita Barger, Denise Griffin, Dave Krehbiel, Jennifer Vise, Steve Kneeshaw.

4.   A man was changing a tire when he stumbled and kicked the hubcap holding t(he four nuts holding the tire in place, and they all rolled into a nearby sewer drain.  Just as he was cursing his fate, a passing boy made a suggestion which enabled the man to drive off (in his own car).  What was the boy’s idea? Take one nut from each of the other three wheels, leaving all four tires with 3 nuts, easily enough to safely drive to a station. Anita Dixon, Mike Brown, Rita Barger, Jim Waterman, Denise Griffin, Dave Krehbiel, Jennifer Vise, Christine Porter, Steve Kneeshaw.

Posted 11/9/15:
5.  Before Mt. Everest was discovered, what was the tallest mountain in the world? Mt. Everest 🙂 Anita Dixon, Mike Brown, Rita Barger, Denise Griffin, Dave Krehbiel, Jennifer Vise, Steve Kneeshaw.
6.  The day before yesterday, Chris was 27 years old.  Next year, he’ll turn 30.  How is this possible? His birthday is 12/31.  Today is Jan 1.  So the day before yesterday (12/30), he was (still) 27.  Yesterday, he turned 28.  At the end of this year (12/31), he’ll turn 29, and next (calendar) year, he’ll turn 30.     Mike Brown, Anita Dixon, Rita Barger, Denise Griffin, Dave Krehbiel, Jennifer Vise, Steve Kneeshaw.
7.   (Suggested by subscriber Mike Brown).  A fish’s length is 8 inches plus half its length.  How long is the fish?  16 inches.  (It can be deduced from the wording that half the fish’s length is 8 inches.) Mike Brown, Anita Dixon, Rita Barger, Dave Krehbiel.
Posted 11/16/15:
8.  How much is 30 divided by 1/2 plus 3?  63. Mike Brown, Anita Dixon, Rita Barger, Jim Waterman, Denise Griffin, Dave Krehbiel, Jennifer Vise, Steve Kneeshaw.
9.  The king of Persia is giving his new minister of interior defense a tour of the city.  As they are walking the king points at a beggar with a donkey and says “that man is the richest man in the city apart from me”.  The minister asks how and the king replies that he seems to be smuggling something but we don’t know how or when he does it.  The minister makes a plan to have the guards search the man whenever he goes in or out of the city, but this plan doesn’t work.  What does the man smuggle?  Donkeys.  Mike Brown, Anita Dixon, Rita Barger, Denise Griffin, Dave Krehbiel, Steve Kneeshaw.
10.  If you had to swallow a pill every half-hour, how long would it take you to swallow three pills?  One hour. Mike Brown, Anita Dixon, Rita Barger, Jim Waterman, Denise Griffin, Dave Krehbiel, Steve Kneeshaw.
Posted 11/23/15:
11.  What day would yesterday be if Thursday was four days from day after tomorrow?  Thursday. Anita Dixon,  Denise Griffin, Dave Krehbiel.
12.  If you were to rip pages 48-54 out of a book,  how many sheets of paper would you take out? Four Anita Dixon, Rita Barger,  Denise Griffin, Dave Krehbiel.

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BONUS

What size container would it take to hold 5000 gumballs, each of which has a 0.5-inch diameter?

(For subscriber Janet Garrett, this was a ‘real world’ problem, and she sent the problem to me.  I believe I got an answer for her, but I had so much fun, I decided to share.  Solutions are not expected to be EXACT, just reasonable, and suitable for the ‘real world’ solution.  PRIZES will be awarded for correct solutions.)

For Campbell’s Proposed Solution, see BT.Bonus.Soln?

Submissions by Denise Griffin and Rita Barger.

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Answers For BT #15-14, Posted throughout October 2015

REMINDER: Answers in red.  Solvers (submitted) in blue.  For further elaboration, feel free to ask!

Please forgive any oversights. It’s a little harder to keep track over a whole month.

Posted 10/5/15:
1.  Homer’s mother has four children.  Three of the children are named Spring, Summer, and Autumn.  What is the name of the 4th child?  Homer.  🙂  Anita Dixon, Jim Waterman, Jeff Campbell, Steve Kneeshaw, Rita Barger, Amy Ragsdale, Jan Garrett, Bobbi Kneeshaw.
2.  What do the following birds have in common?  cardinals, eagles, falcons, ravens.   The ‘intended’ answer was that they are all mascots of NFL teams, but SEVERAL submitters found other good answers:  Second letter is a, each has two (and only two) different vowels, each bird has historical significance in other countries (with examples!).  Good jobs!!    Anita Dixon, Jim Waterman, Jeff Campbell, Jan Campbell, Steve Kneeshaw, Rita Barger, Amy Ragsdale, Bobbi Kneeshaw.
3.  Horace Jordan was born in February 1896.  Why did he only celebrate his first birthday in 1904? Horace was born on Feb 29, 1896.  Since 1900 was NOT a leap year (‘century years’ need to be divisible by 400), he did not celebrate his next ‘birthday’ until 1904.    Anita Dixon, Jim Waterman, Jeff Campbell, Steve Kneeshaw, Rita Barger, Amy Ragsdale, Bobbi Kneeshaw.
Posted 10/12/15:
4.  In how many states is it legal for a man to marry his widow’s sister? Well, since for a man to have a ‘widow’, he must be dead, it’s not likely.  Subscriber Jim Waterman, however, submitted more than one Comment about this one (Comments are now active/posted), and found two states that allowed it under unique circumstances.  Anita Dixon, Jim Waterman, Rita Barger, Amy Ragsdale.
5.  Erin’s plane left New York at 11 AM for her five-hour flight to LA.  Assuming punctuality, what time did she arrive? Accounting for time zones, she arrived at 1 PM, Pacific time.    Anita Dixon, Jim Waterman, Bobbi Kneeshaw.
6.  J.J.J. Smith has an 85 average on his four tests in Calculus.  The final is the same weight as each test – all are 100 points.  What will he need to score on the final, to bring his grade up to an A (90 average)?  Can’t be done, unless you allow extra credit (as some suggested).  He would need to score 110 points to get to a 90 average.  Anita Dixon,  Rita Barger.
Posted 10/19/15:
7.  Matt often goes the wrong way on a one-way street – right in front of a police station!  Why is he never arrested? Matt is walking.  Anita Dixon, Jim Waterman, Rita Barger, Amy Ragsdale.
8.  Batty Benny has a bizarre book.  The foreward comes after the epilogue.  The end is in the first half, and the index is placed before the introduction.  You may have this book, too.  What is it? A dictionary.  Anita Dixon, Rita Barger.
9.  If you write down every whole number (integer) between 50 and 100, how many times will you write the digit 6? 15 times (don’t forget the 60s).  Anita Dixon, Rita Barger.
10.  In how many ways can two dice be rolled to yield a sum divisible by 3?  Twelve (12) ways.  All submitters mentioned/questioned the problem of ‘order’, so there are multiple answers depending on interpretation.  Typically, getting 3 by rolling a 2-1 or 1-2 is considered TWO different ways.  (Think of having a red die and a blue die), but I also took answers that only considered that one way.  Anita Dixon, Jim Waterman, Rita Barger.  

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Answers For BT #15-13, Posted throughout September 2015

REMINDER: Answers in red.  Solvers (submitted) in blue.  For further elaboration, feel free to ask!

I may have missed some submitters this time :-(.  Please forgive oversights.

Posted 9/7:  Three”Real World” Brain Teasers Where Math Can Help 🙂

1. Ralph found an ad for a lot that was advertised as ‘one acre by one-half acre’ in a marvelous location at a reasonable cost, yet he was a little reluctant to follow through.  Why? An acre is a measure of area already, not length.  The phrasing above is confusing at best, inaccurate at worst.  Anita Dixon, Rita Barger, Jim Waterman
2. A professional sports team was in salary cap trouble.  The General Manager approached the team’s star, Willy Ketchem, with the following offer:  Please help us out this year by taking a 25% pay cut for this next year only.  If you’ll do that, we promise to give you a 30% raise the following year.  Willy was willing (say that three times quickly!), but his agent advised against it – for mathematical reasons.  Why is that?  No matter the amount, these two transactions will result in a figure that is only 97.5% of where he started.  Consider $100.  25% cut yields $75.  But a 30% raise (of $75) only gets back to $97.50.  Rita Barger, Jim Waterman
3. Why are manhole covers round?  Wouldn’t rectangular ones be easier to build? (There is an important mathematical reason for this!)  Round manhole covers will NOT fall back down into the hole – and onto workers! – as other (normal) shapes could!  Rita Barger, Jim Waterman

Added 9/14:  A couple of more traditional goodies:
4.   A car dealer sold 60 cars during a six-day sale.  Each day, he sold 4 more cars than he did the day before.  How many cars did he sell on              the first day?  None.  ( 0 + 4 + 8 + 12 + 16 + 20 = 60).  Rita Barger, Jim Waterman
5.  Which has more area – a square of side 1, or a circle with diameter 1? The square.  (1 square unit vs. approx .785 sq. units).   Rita Barger, Jim Waterman
Added 9/21:  BTs concerning Time Zones 🙂
6.  When it comes to time zones, the countries of China and India share an interesting fascinating fact.  What is it?  Each country only has ONE time zone.  (Countries have jurisdiction.)  All of China follows Beijing – which makes for HUGE weird disparities!!  India started the practice during British era, to standardize train times in the country.  Mike Brown knew the answer for China, as they have Chinese foreign exchange students from MSU currently living with them.
7.   How do time zones work at the North and South Poles, where all the longitude lines converge?  At the North Pole, where there are several research stations, each station uses the/a time of their home country.  At the South Pole, only the US has a research station, but they use the time of Christchurch, New Zealand, as that’s where flights to the base leave from.
8.   And, finally, how does the International Space Station keep its time?  It uses Greenwich Mean Time.
Added 9/21: Special Dates
9.  a)  What was mathematically special about the second Saturday of this month (9/12)?   b)  This phenomenon will occur only ONCE more this century!  When?  Why is it the last?  My own intended answer:  9/12/15 forms 3 consecutive multiples of 3, which will only happen again on 12/15/18, since the month number would be bigger than 12 after that.  RITA BARGER had another answer, and in my opinion, MUCH cooler!!  9/12/15 is a “Pythagorean Triple” – the sides of 9, 12, and 15 would form a right triangle (since they are multiples of 3,4, & 5).  And THAT will only happen again in 12/16/20 (for the same reasons)!!  GREAT OBSERVATION, Rita!!  🙂

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 Answers For BT #15-12, Aug 10 & 24, 2015

REMINDER: Answers in red.  Solvers (submitted) in blue.  For further elaboration, feel free to ask!

1.  Old MacDonald had some hens and some rabbits.  Together, these animals have eight heads and twenty-two feet.  How many of each did Farmer Mac have?    5 hens, 3 rabbits.   Anita Dixon, Rita Barger, Amy Ragsdale, Bobbi Kneeshaw, Jim Waterman.
2.  Al, Bob, Carl, and Dave were standing in line.  Dave was not first.  Bob was between Al & Carl.  Al was between Dave and Bob.  In what order were they standing in line?    Carl, Bob, Al, Dave.   Anita Dixon, Rita Barger, Amy Ragsdale. (Bobbi Kneeshaw and Jim Waterman switched Al & Bob, but were otherwise right.)
3.  You  lost your place in the book when you dropped it on the floor, but for some reason, you remembered that the product of the pages is 16,002.  (Yeah, I know!  Just play along.  :-))  What are the page numbers?   126 & 127.    Anita Dixon, Rita Barger, Amy Ragsdale, Bobbi Kneeshaw, Jim Waterman.
4.  Pick any two-digit prime number.  It turns out the the number on one side or the other of the prime will be divisible by 6.  Why?  Neither number can be odd (the prime is), so they’re both divisible by 2.  Also, in any three consecutive integers, one of them is divisible by 3 – and again it can’t be the prime.  So ONE of the numbers on either side is even and divisible by 3, which makes it divisible by 6.    Anita Dixon, Rita Barger, Jim Waterman.
***
5.  Find a three-digit perfect cube whose digits add to a perfect square.  (Hint: there aren’t many possibilities.)  216.  Anita Dixon, Rita Barger
6. (Have I done this one before?)  What are the next three letters in this common sequence:  O, T, T, F, F, S, S, __, __, __ ?   E(ight), N(ine), T(en).  Anita Dixon, Rita Barger
7. (For Math Nerds?)  A “20 inch” bicycle has wheels with a radius of 10 inches.  How many revolutions (roughly) do the wheels make in a mile ride?  The circumference of the wheel (C = pi*d or 2*pi*r)  is approximately 62.8 inches.  A mile is 63,360 inches.  So the wheel makes approximately 1009 revolutions. Anita Dixon, Rita Barger

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Answers For BT #15-11, July 20, 2015

REMINDER: Answers in red.  Solvers (submitted) in blue.  For further elaboration, feel free to ask!

1.  Loaded Questions, Part 2.   More not-as-easy-as-they-might- look questions.  Think twice.

a.   Who said “Everybody talks about the weather but nobody does anything about it.”?  The remark was made by Charles Dudley Warner, a friend of Mark Twain’s, but not by Twain himself.  Anita Dixon

b.   Which of the following rid Ireland of the snakes?  a)  The Royal Zoological Society, b)  Nobody – there were never any snakes there,   c)  Irish terriers, d) St. Patrick.  Anita Dixon.

c.  How much more reflected light do we get from a full moon than from a half-moon?  Twice as much?  About the same?  Four times as much?  Seven times as much?  Although Anita says 11 times as much, and I probably trust her more than my source! 🙂  Anita Dixon.

d.   Where was the Battle of Bunker Hill fought?  On nearby Breed’s Hill.  Anita Dixon

2.    What are the two missing letters?  I  V  X  L  _C_  _D_  M  (Think Roman numerals.)  Anita Dixon, Rita Barger.
3.  What is the 117th odd natural number?  233.    Anita Dixon, Rita Barger.
4.  What is a particular number if 1/2 of it plus 2/3 of it add to 42? 36.   Anita Dixon, Rita Barger.
5.   Can you find 5 consecutive integers, none of which are prime?  YES.  🙂  In fact, there are LOTS of places where this occurs.  The first time it happens is at 24, 25, 26, 27, and 28. Anita Dixon, Rita Barger.  For more information here, see today’s Math Tidbit, and/or the further explanation at Consecutive Composites.

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 Answers For BT #15-10, July 6, 2015

REMINDER: Answers in red.  Solvers (submitted) in blue.  For further elaboration, feel free to ask!

1.  Loaded Questions, Part 1.  (more in future BTs)  These are not as easy as they look.  Think twice.

a.   Adam and Eve were banished from the Garden of Eden for eating what fruit?  The exact fruit is not specified. (‘fruit of the knowledge of good and evil’).  Anita Dixon, Rita Barger.

b.   How many of each animal did Moses take onto the Ark?  Noah ‘captained’ the Ark, not Moses.  (Or more precisely, Moses took NONE onto the Ark.)   Anita Dixon, Rita Barger, Amy Ragsdale.

c.  What was the highest title Julius Caesar acquired:  king, emperor, dictator, or consul?  Julius Caesar was named dictator for life, but never held the title of emperor, which was not even created until years after his death.  Rita Barger

d.   Does England have a 4th of July?  Of course.  🙂  They just don’t celebrate it as we do.     Anita Dixon, Rita Barger, Amy Ragsdale.

2.  Find the next two numbers in this sequence:  2, 3, 5, 9, 17, ___, ___.  (Multiple ‘correct’ answers here?)  Most probable answers are 33 & 65 (differences of 1, 2, 4, 8, . . .).   Anita Dixon, Rita Barger, Amy Ragsdale.
For #3 & 4, it is helpful to look at (or quickly jot down) all sixteen (16) possibilities for the outcomes.
3.  If a couple plans to have four children, which is more probable:  a) 2 boys, 2 girls, or b) 3 of one sex, 1 of the other?  Interestingly, of the 16 outcomes, only 6 are 2B, 2B, while 8 are 3 of one sex, 1 of the other.  So the latter is more likely.   Anita Dixon, Rita Barger.
4.  See #3 above.  How likely is it the couple’s children will all 4 be of the same sex?  Only 2 of the (16) ourcomes are 4 of each sex, so the liklihood (probability) is 2/16 or 1/8.  Anita Dixon, Rita Barger.

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Answers For BT #15-9, June 15, 2015

REMINDER: Answers in red.  Solvers (submitted) in blue.  For further elaboration, feel free to ask!

1.  How are the following numbers arranged?    2   3   6   7   1   9   4   5   8   Reverse alphabetical order of corresponding words.  Anita Dixon, Rita Barger.
2.  What’s the fewest amount of coins needed to pay for anything that might be priced less than a dollar?  (1 cent to   99 cents.) Nine, namely 4  pennies, 1 nickel, 2 dimes, and 1 quarter, and 1 half-dollar.  Anita Dixon, Rita Barger.
3.  (A long time ago!) a man went into the post office clerk, and – offering a dollar – said, “Give me some 2-cent stamps, ten times as many 1-cent stamps, and the balance in 5-cent stamps.”  How can the clerk meet this request?  The man was given five 2’s, fifty 1’s, and eight 5’s.  Anita Dixon, Rita Barger.

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Answers For BT #15-8, June 1, 2015

REMINDER: Answers in red.  Solvers (submitted) in blue.  For further elaboration, feel free to ask!

1.  “I guarantee”, said the pet salesman, “that this parrot will repeat every word it hears.”  A customer bought the parrot but found it would not speak a single word.  Nevertheless, the salesman told the truth.  Can you explain?  The parrot was deaf.  🙂  Anita Dixon, Rita Barger.
2.  Find the sum of the reciprocals of all the whole-number factors of 24.    1/1 + 1/2 + 1/3 + 1/4 + 1/8 + 1/12 + 1/24 = 60/24 = 2.5     Anita Dixon, Rita Barger.
3.  What is the largest three-digit number divisible by both 7 & 9?    945     Anita Dixon, Rita Barger.
4.  If a jar of peanut butter that is 3 inches in diameter and 4 inches high sells for 60 cents (ha!), what is a fair price for a jar that is 6 inches in diameter and 6 inches high?   Volume of larger jar is 6 times that of the smaller jar [ask for details, if desired], so a fair price – disregarding cost of containers- would be $3.60.    Anita Dixon.

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Answers For BT #15-7 & 15-7.5, Apr 6 & 13, ’15

REMINDER: Answers in red.  Solvers (submitted) in blue.  For further elaboration, feel free to ask!

1.  What’s a good method to solve this problem mentally?   (2015 + 2015) x 50  2015 + 2015 = 2*2015.  So, we could think 2*2015*50 = 2*50*2015 = 100*2015 (= 20150).

2.  Next year (2016) is a leap year.  On what date next year will 2/3 of the year have elapsed? Aug 31.  Anita Dixon.
3.  Use these clues to figure out the year the first US transcontinental railroad was completed:  1869. Anita Dixon.

a.  The sum of the digits is 24.

b.  The ones and the tens digits are multiples of 3.

c.  The hundreds digit is 1 less than the ones digit.

4.  The centers of fence posts are 30 inches apart.  They enclose a triangular region 20 ft x 20 ft x 10 ft.  How many posts will be needed?  20 fence posts.  Anita Dixon.
Held over from last week:
5.  If the digit 7 is written at the right of a certain number, that number is increased by 70,000.  Find the number. 7777.
6.  How many whole numbers are between the square roots of 8 & 80?  Six.  (3,4,5,6,7,8)  Anita Dixon.
7.  The number 6, say, has 4 whole-number divisors: 1,2,3,and 6.  What is the smallest number with exactly FIVE whole-number divisors?  16.  (1,2,4,8,16)  Anita Dixon.
8.  Take a person with a pulse rate of 72 beats/minute.  How many times will his/her heart beat in April?  72x60x24x30 = 3,110,400  Anita Dixon.

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Answers For BT #15-5 & 15-6, Mar 2 & 9, ’15

1.  How many three digit numbers consist of only odd digits?  Is the answer the same for even digits?  For the only-odd digits, there are 5*5*5 = 125 such numbers.  Since a leading digit of 0 is not really a three digit number (We write 046 as 46) – and since 0 IS even, that leaves, 4*5*5 = 100 options for all-even digits.
2.  Why/when is FOUR half of FIVE?  (Hint:  It’s the middle half!)  Using Roman numbers, look at the IV in the middle ‘half’ of the word FIVE.  🙂 
3.  Using the numbers 3,3,7, and 7, along with any of the +, -, x (or *), /, and parentheses, obtain a total of 24.  (There are at least 2 ways to do this – maybe more.)  Here is one: (there are likely more?) (3 3/7) x 7  
4.  If nine thousand nine hundred and nine dollars is written as $9909, how should twelve thousand twelve hundred twelve dollars be written?  $12,312  🙂  
HELD OVER FROM 3/2/15:
5.  Susan and Lisa decided to bet on their tennis games over the course of one week.  They bet $1 on each game.  Susan won three bets and Lisa won $5.  How many games did they play that week?  Eleven games.
6.  Sometimes the numbers displayed on a digital watch are in consecutive order, as in 2:34.  How many times does this happen in a 12 hour period?  (Note:  I personally think there are [at least] two different ‘correct’ answers here, depending on your definitions.  I’ll gladly take either if your explanations match.)  Four or eight, depending on your condition.  1:23, 2:34, 3:45, and 4:56  and – if you count them (which I do) 9:10, 10:11, 11:12, and 12:13.  (Would you count 1:02, 2:03, . . .?)
7.  Still on the subject of watches:  A man set two watches to the same time at midnight.  He soon discovered that one of the watches was running 2 minutes/hour too slow and the other was running 1 minute/hour too fast.  Later the same day, the faster one was exactly one hour ahead of the other one.  What time was it?  The watches get 3 minutes further apart each hour.  So in 20 hours (at 8 PM), they’ll be 60 minutes apart.
8.  What can be purchased at a hardware store that would be priced as follows (with no bulk pricing discounts)? 1 costs $1,  12  costs $2, &  144 costs $3 ?  The items are house numbers, which were going for $1 apiece.
9.  If we’re asked “How many squares on a standard 8 x 8 checkerboard?”, our immediate answer might be 64.  But those are just the ‘small’ squares.  🙂  There are other sized squares as well.  So, how many squares (of any size) are on a checkerboard?  204.  Some absolutely beautiful patterns here. 🙂

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Answers and Information on BT #15-4, Feb 18, ’15

1.  Several years ago, I drove a nail into a tree exactly five feet above the ground.  The tree grows at a rate of one half-foot per year.  Last year, 11 years later, I returned and saw the tree. How far above the ground was the nail?  5 feet.  Trees grow from the top.  (Another insight here provided by Kurt Killion’s Comment/Clue on the BT post – what about fence nailed to tree?).  Jeff Campbell (newcomer!), Ann Gray (newcomer!), Steve Kneeshaw, & Rita Barger.  Added later:  AND Alexis Avis’ 3rd & 4th Grade classes!!  For their thoughts see Alexis’ Class’ Solution.  (There’s a link there to get you back here.) 2.  The volumes of Gibbon’s Decline and Fall of the Roman Empire stand side by side on a bookshelf (Vol I to the left of Vol II, etc).  A bookworm starts at page 1 of Volume I and bores his way in a straight line to the last page of Volume II.  If each cover is 1/8 inch thick, and each book with the covers is 2 inches thick, how far did the book worm travel?  1/4 inch only.  NOTE the position of the books (where’s page 1?) !  Both the pages in question are ‘in the middle’ of the two books. The bookworm only went through two covers.  🙂  Jeff Campbell and Rita Barger.    3.  A bear left its den and walked straight south for 1 mile.  Then it turned left (right angle) and walked another mile.  Finally it turned left again, and walked one more mile – arriving right back at its den!  What color was the bear – and why?  The only place on the planet the above can be done is starting at North Pole.  So (presumably) the bear is a Polar Bear and therefore white.  Jeff Campbell, Steve Kneeshaw, Rita Barger.

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Answers and Information on BT #15-3, Feb 9, ’15

1.  If a year had two consecutive months with a Friday the 13th, what two months would they have to be?  (Why?)  February and March (as this year!!).  In non-leap years, Feb has 28 days, making exactly four weeks, so March starts (again) on the same day as Feb.  If you have a Fri 13th in Feb (in non-leap years), you’ll have one in March, too.  Anita Dixon, Mike Brown, Jim Waterman, Alexis Avis. 2.  Find four consecutive whole numbers that add up to 178.  43, 44, 45, and 46.  (Trial/error may be fastest approach!).  Anita Dixon, Mike Brown, Jim Waterman, Alexis Avis. 3.  How many cards must be drawn from a standard deck of (52) playing cards to be sure that you have at least two cards from the same suit?  Five (5).  There are four suits, so at ‘worst’, the first four cards will be from different suits.  So, if you haven’t duplicated by then, the fifth card must duplicate a suit.  Anita Dixon, Mike Brown, Jim Waterman, Alexis Avis. 4.  What part of a 1/2 square foot is a 1/2 foot square?  Half.  🙂  An interesting problem!  A square that is 1/2 ft. on each side has an area of 1/4 sq. ft. (1/2 x 1/2).  So, a ‘1/2 foot square’ is half of a ‘1/2 square foot’. !  Anita Dixon, Mike Brown, Jim Waterman, Alexis Avis. 5.  The average (mean) of three test scores is 74.  What must the fourth test score be to increase the average (mean) to 78?  90. (  [74 + 74 + 74 + 90] / 4 = 78. )  Anita Dixon, Mike Brown, Jim Waterman, Alexis Avis.

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Answers and Information on BT #15-2, Feb 2, ’15

1.  A murderer is condemned to death.  He has to choose between three rooms.  The first is full of raging fires, the second is full of assassins with loaded guns, and the third is full of lions that haven’t eaten in 3 years.  Which room is safest for him?  Presumably, lions that haven’t eaten in 3 years are long since dead.  🙂  That room’s probably his safest choice.   Answered ‘correctly’ by Anita Dixon, Mike Brown, and Bobbi Kneeshaw. 2.  Can you name three consecutive days without using the words Monday, Tuesday, Wednesday, Thursday Friday, Saturday, or Sunday, or any of the months of the year?  Interesting answers here.  The source I used for this one was looking for “yesterday, today, and tomorrow”, and I got that.  But I gave ‘full credit’ 🙂 to “Labor Day Weekend” and “Christmas, the day before, the day after” or similar.  Anita Dixon, Donna Majetic, Steve Kneeshaw, Mike Brown, and Bobbi Kneeshaw. 3.  A man and his son are in a car wreck, and are taken to different hospitals.   At the emergency room of the hospital where the boy was taken, the attending physician gasps and says ” I can’t work on this patient – he’s my son!”  How can this be? The doctor was his mother! (I think it’s a good sign that folks get this MUCH faster these days than they used to when I first started using it.)  Anita Dixon, Donna Majetic, Steve Kneeshaw, Mike Brown, and Bobbi Kneeshaw. 4.  This is an unusual paragraph.  I’m curious how quickly you can find out what is so unusual about it.  It looks so plain you would think nothing is wrong with it.  In fact, nothing is wrong with it!  But it is unusual, though.  Study it, and think about it, but you still may not find anything odd.  But if you work at it a bit, you might find out.  Try to do so without any coaching!  The letter ‘e’ does not appear at all in the above paragraph!  Anita Dixon & Mike Brown. 5.  Ralph is trying to limit his coffee input, so he alternates days of drinking coffee and hot tea. He drinks coffee on odd-numbered mornings, and hot tea on even-numbered mornings.   Further, he always allows himself coffee on Mondays, regardless of date. He’s discovered that under these conditions, there are occasionally circumstances in which he could drink coffee for four straight days.  Can you deduce those circumstances? At least 2 answers here (and I got both).  If a 31-day month has a Saturday fall on the 31st (as just happened), then that day starts 4 days that will work (since the 2nd is a Monday).  OR, if a 31-day month ends on a Tuesday, that Tuesday will be the third of four straight days that will ‘work’.  Anita Dixon, Steve Kneeshaw, Mike Brown, & Bobbi Kneeshaw.

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Answers and Information on BT #15-1, Jan 19, ’15

1.  I am a word with six letters.  When one letter is removed, I am now 12.  What word am I?  DOZENS. Removing the ‘s’ gives dozen, or 12.  Answered by Anita Dixon, Mike Brown, Bobbi Kneeshaw, Steve Kneeshaw, Rita Barger, and Donna Majetic (1st time submitter!) 2.  Find a 5-digit number where the sum of all the digits is 25, and each digit is 2 more than the digit preceeding it.  13579.  Anita Dixon, Mike Brown, Bobbi Kneeshaw, Steve Kneeshaw, Rita Barger, and Donna Majetic  3.  What number is 20 more than twice the number that is 10 more than 15 times one-half of ten?  190.  Anita Dixon, Mike Brown, Bobbi Kneeshaw, & Steve Kneeshaw 4.  You have 12 coins in front of you, knowing that one of them is counterfeit.  All you know is that the ‘bad’ coin is slightly heavier than the others.   You also have a balance scale in front of you, and your task is to determine the ‘bad’ coin using only three (3) weighings.  How do you accomplish this? There were TWO different (correct) approaches by solvers.  The majority split the coins into 2 piles of six.  Take the heavier pile and split into 2 piles of 3.  Take the heavier of those and put one on each side.  If they balance, the remaining coin is bad.  If they don’t the ‘heavier’ one is bad.  Rita Barger chose to use 3 piles of 4, and also was successful.  (Can you figure out how?)  Anita Dixon, Mike Brown, Bobbi Kneeshaw, Steve Kneeshaw & Rita Barger. 

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Answers and Information on BT #10 – 12/1/14

1.  Three mothers have two daughters apiece.  If they all live together and all want a separate bedroom, what’s the smallest number of bedrooms that might accommodate them?  Consider one mother, her two daughters, and each of their two daughters.  There are then 3 mothers, each having 2 daughters, but there are only 7 women.  So it can be done with 7 bedrooms. Correct answers by Alexis Avis, Rita Barger, and Anita Dixon. 2.  It was bright and sunny at 12 noon today.  What’s the probability it will be sunny again 60 hours from that time (in the same location)?  In 60 hours, it will be midnight.  So for most places, there’s no chance.  Alexis Avis, Rita Barger, and Anita Dixon. 3.  Take the first 100 primes and multiply them all together.  What would be the digit in the ones (units) place of the product?  [This is easier than it looks.]  Zero (0).  After multiplying the first 3 primes (2,3, & 5), the product is 30.  After that, no matter what else is multiplied, there will still be a 0 at the end.  Alexis Avis, Rita Barger, and Anita Dixon. 4.  A man was changing a tire when he stumbled on the hubcap holding all the nuts holding the tire in place and they all fell into a nearby sewer drain.  Just as he was cursing his fate, a passing boy made a suggestion which enabled the man to drive off (in his own car).  What was the boy’s idea?  Take one nut off each of the other 3 tires, and use them to put on the 4th tire, and this will allow the man to drive off safely.  Rita Barger and Anita Dixon. 5.  SANTA–THEMED closing shots. OK,  these are pretty grade-school corny, but . . . . . 🙂

A.  In what month does Santa eat the least?  February – it has the fewest days.  🙂  Josh Walters and Rita Barger.

B.   At the North Pole, you cannot take a picture of an elf with a red shirt.  Why not?  Red shirts will not take pictures.  You must use a camera.  (Ouch).  Josh Walters, Alexis Avis, Anita Dixon.

C.  What do you call a reindeer with three eyes?  A reiiindeer.  Josh Walters, and credit to Rita Barger and Anita Dixon for ‘mispelled’.  🙂

D.  What do reindeer have that no other animals on earth have?  Reindeer babies.  Josh Walters, with credit to Alexis Avis for ‘reindeer mothers.’

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Answers and Information on BT #9 – 11/10/14

1.  Thursday 11/13, was one of only THREE (3) Twin Prime Days in any year.  What are the other two twin prime days each year?  3/5 (Mar 5) and 5/7 (May 7)  Correct answers submitted by Anita Dixon, Rita Barger, and Steve Kneeshaw. 2.  Ralph drives 60 miles at an average speed of 30 mph (fog maybe?), then returns over the same route at an average speed of 60 mph.  What is his average speed for the entire trip?  Ralph drives 120 miles in 3 hours, so his average speed is 40 mph (not 45, as often assumed.)  Anita Dixon, Rita Barger, and Steve Kneeshaw 3.  What are the next two letters in this sequence?          O, T, T, F, F, S, S, ___, ___   E, N.  Using first letters of numbers, we have:  One, Two, Three, Four, . .   🙂  Anita Dixon, Rita Barger. 4.  Painted Cube  A wooden cube is dropped into red paint.  It is then cut into 27 equal-size smaller cubes (3 equal cuts each direction – like a Rubik’s Cube).  How many of the smaller cubes are found to have red paint on a) 3 faces,  b) 2 faces,  c) 1 face, and  d) no faces?  8,12,6, and 1, respectively. Anita Dixon, Rita Barger, and MACY MIDDLETON (5th grade student of Alexis Avis.)  (For a picture of Macy’s work, see Macy’s Painted Cube Solution.) 5.  Let’s suppose that – flush with the elation of my Royals’ success in ’14  – I make this foolish bet:  I’ll take the SUM (add them up) of all the Royals‘ game scores next season, and I’ll give you the PRODUCT (multiply them!) of all the Cardinals’ game scores next season, and I’ll bet my number is higher!  Foolish bet?  How likely would I be to win?  Fairly likely.  🙂  If the Cardinals get shut out (score no runs) in even one game (not unlikely, even for the Cardinals), their product for the whole season will still be 0, making it sure (or almost) for me to win.  Anita Dixon, Bobbi Kneeshaw, Rita Barger.

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Answers and Information on BT #8 – 10/27/14

1.  The beginning of eternity, the end of time and space;  the beginning of every word and the end of every place.  What is it? The letter ‘e’.  🙂  Correct answers by Josh Walters, Mike Brown, Rita Barger, Anita Dixon, Tammy Stine, and Donna Majetic. 2.  What is the only number that is spelled (in English) with the exact number of letters as the number being spelled? Four.   Josh Walters, Mike Brown, Rita Barger, Anita Dixon, Tammy Stine. 3.  Taken from an old DOTS box:  A candy dish is filled with red, yellow, and green Dots.  If you eat the red Dots first, there would 4 Dots remaining.  If you eat the yellow Dots first, there would be 4 Dots remaining.  If you eat the green Dots first, there would be 4 Dots remaining.  How many of each each color are in the candy dish? Two of each color, for a total of six (6).    Mike Brown, Rita Barger, Anita Dixon, Tammy Stine.

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Answers and Information on BT #7 – 10/20/14

1.  A young tot answered the phone and asked who was calling.  “I married your mother, but I am not your father – or your stepfather!”  the man replied.  Who was calling? The minister, priest, rabbi, etc that performed the tot’s mother’s ceremony.  Correct answers received from Steve Kneeshaw, Bobbi Kneeshaw, Rita Barger, Richard Barger, and Tammy Stine. 2.  Using only pennies, nickels, dimes, and quarters (but at least ONE of each), make change for $1.00, using exactly fifty coins. One quarter, 2 dimes, 2 nickels, and 45 pennies.  Correct answers received from Steve Kneeshaw, Bobbi Kneeshaw, and Rita Barger. 3.  A digital clock forms palindromic numbers* 114 times a day.  What is the least time between two consecutive palindromic clock numbers?  What is the most? 2 minutes – between 9:59 and 10:01 (Rita Barger and Tammy Stine) and 70 minutes – between 10:01 and 11:11 or between 11:11 and 12:21. (Rita Barger).

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Answers and Information on BT #6 – 10/6/14

0.  (Carry-over from last week).  John and James are twins (to each other).  John celebrated his fourth birthday today, and James celebrates his first birthday tomorrow.  How can this be – and what day of the year must it be?? John was born just before midnight on Feb 28 in a leap year, and James was born just after midnight (on Feb 29).  Correct answers received from Jeff Campbell, Bobbi Kneeshaw, Steve Kneeshaw,  Rita Barger, and Tammy Stine. 1.  (An old classic)  A frog is at the bottom of a 30 foot well.  Each day she is able to jump up 5 feet, but during the night, she slides down 3 feet.  How many days will it take her to jump out of the well?  [Let’s just ignore the fact that she might starve to death first.  :-)]  After 13 days, the frog is at 26 feet.  So, on the 14th day, the frog jumps out (and therefore does not slide back down.) Answered correctly by Rita Barger and Tammy Stine. 2.  Mary has a new car with four new tires (duh!) , and one new fully functional spare tire.  She has the tires rotated regularly, so that after 100,000 miles each tire will have been driven the same number of miles.  For how many miles will each tire be used? 80, 000 miles wear on each tire.  Correct answer by Rita Barger. 3.  (One of my VERY favorites!!)  Mr. Smith says ‘Brothers and sisters have I none, but this man’s father is my father’s son.”  What is the relationship between Mr. Smith and the person to whom he refers? Mr. Smith is speaking of his son.  Solved by Rita Barger and Tammy Stine.

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Answers and Information on BT #5 – 9/29/14

So many interesting (and absent-minded) things occurred here last week, that I’m going to blend answers, winners, and comments into the actual BTs – see below.

1.  What is the only number whose letters of its spelling appear in alphabetical order? FORTY.  Correct answers from Jeff Campbell, Anita Dixon, and Bobbi Kneeshaw.  (And Mike Brown wins the ‘creative award’ for suggesting that in Spanish, the answer might be dos (two) !  🙂 Is ‘dos’ the only one?) 2.  What is the only number whose letters of its spelling appear in reverse alphabetical order? ONE. Correct answers submitted by Jeff Campbell, Anita Dixon, and Mike Brown. 3.  What is the first number whose spelling contains an ‘a’. One thousand. Correct answers submitted by Jeff Campbell, Anita Dixon, Mike Brown, and Bobbi Kneeshaw.  Bonus Quickie:   John and James are twins (to each other).  John celebrated his FOURTH* birthday today, and James celebrates his first birthday tomorrow. *Corrected Tuesday AM (9/30).  🙂 How can this be – and what day of the year must it be?? My KEYBOARD (!!) goofed again!!  The Bonus was supposed to read as above in green (and as corrected on Tuesday), but I suspect not many saw that in time.  There were SEVERAL correct ‘answers’ and interpretations to the earlier statement (which had first rather than fourth) and I have had ONE correct solution (from Bobbi Kneeshaw) already to the statement above.  WE WILL LEAVE THIS OPEN ONE MORE WEEK.

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Answers and Information on BT #4 – 9/15/14

1. The 22nd and 24th presidents of the United States had the same mother and the same father, but were not brothers.  How could this be so?  Grover Cleveland was the 22nd President.  AND the 24th!  🙂  He has been the only president (so far) to serve two non-consecutive terms.   2.  A man who was not wearing a parachute jumped out of a plane.  He landed on hard ground, yet he was unhurt.  Why?  The plane was still on the ground.  🙂 Correct answers to #1 and #2 were received from Donna Majetic, Steve Kneeshaw, Becky Austin, and Anita Dixon.  A correct answer to #2 was also received from Linda Hobbs. I’m delighted because almost all of these names are new ‘solvers’ !!

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Answers and Information on BT #3 – 9/1/14

1.  The two coins are a quarter and a nickel.   One of the coins is not a nickel.  The other is.  [I know, I know – don’t look at me like that.] 2a.  The only two-digit number divisible by all of 1,2,3,4,5, & 6 is 60. 2b.  The smallest number divisible by all of the first 10 whole numbers is 2520.

Correct Responses (in order of receipt):

1.  Bobbi Kneeshaw, Anita Dixon, Rita Barger, Josie Stone, and Mike Brown. 2a  Anita Dixon, Rita Barger, JoJo Stone, and Mike Brown. 2b. Anita Dixon, Rita Barger, and Mike Brown.

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 Answers and Information on the King & His Subjects BT – 8/18/14

The Royal Alchemist could not have invented a liquid that dissolved everything, as there would be no way to store/hold such a liquid.  It would dissolve the container! How would anyone know (in 55 BC) that it was 55 BC ?!  Thus no such coin could exist, and the Royal Coin Collector had to be guilty of fraud.

There were a couple of late responses (after Thursday noon), but I’m counting them, as these Answers were not published yet.  

Correct answers to BOTH cases of fraud came in from Julie Sperry, Anita Dixon, and Rita Barger (late).  Pat Campbell’s answer (also late) for the Alchemist was correct.  CONGRATS to all.

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Answers and Information on the Horsing Around Brain Teaser – 8/4/14

The Brain Teaser:  A man buys a horse for $60, sells it for $70, buys it back for $80 and sells it once more for $90.  How much did the man make or lose – if any – on the transactions?

The Answer:  The ‘horse trader’ made $20 profit.  There is more than one way to see this, but perhaps the easiest (opinion?) is to note that the man paid out $140 (60 + 80) in the transactions, but received $160 (70 + 90).  This approach was also mentioned by Anita Dixon, as you may have seen. There were FIVE correct answers submitted (all of whom will receive a prize, as noted in last week’s Weekly Photo Specials).  These five were – in order of submission:  Natalie Moon, Josh Walters (both of these received early Monday AM), Pat Campbell (there’s a story here!), Rita Barger, and Anita Dixon.  Congrats to all!! One of the things I love about this Brain Teaser is that I get frequent (pretty good) answers of ‘made $10’ and ‘made $30’ as well.  This makes for good discussions.  In fact, I often contend to teacher groups with whom I work(ed) that I could convince them of all 3 answers.  [ . . the point being needing to have the ability to spot holes in arguments – even good ones!]   If you’d like to hear the arguments, let me know.

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 Answers to questions about dates (and perfect numbers) on 7/28:

1.  The 7 dates every year where (Month) x 4 = (Day) are Jan 4, Feb 8, 3/12, 4/16, 5/20, 6/24, and 7/28. 2.  The 4 dates this year where all 3 digits are multiples of 7 are July 7, 14, 21, and 28, 2014. 3.  The perfect number less than 28 is 6.  (6 = 1 + 2 + 3). As of Friday late afternoon (8/1), only Anita Dixon had submitted correct answers to all questions.