Larry N. Campbell

Pesky Puzzlers 2025

IMPORTANT NOTE:

To submit solutions, it is best to EITHER reply to one of the current mailings OR e-mail them directly to larrycampbell@missouristate.edu.

PP 25.24: Do any or all:

  1. Marco the Mule did not do well in either algebra or geometry, yet when he is tied to his 3-foot rope, he is able to eat from the bucket of oats 6 feet away.  How does he do it?
  2. How many fractions with a denominator of 23 have values between 0.18 and 0.82?
  3. Given that 2/3 of a committee use ¾ of the chairs in a room, what is the least possible number of members on the  committee?
  4. What number should be removed from the following list so that the average of the remaining numbers is 6.8?                    1,2,3,4,5,6,7,8,9,10,11
  5. ONGOING – Can’t Miss Fun!! Find your own Puzzler(s), Brain Teaser(s), Riddle(s), etc. Then submit it/them with the answers and you’ll get credit for this Puzzler! (And, if I use yours here in the future, you’ll be acknowledged.)

Some Previous Puzzlers – and Solutions (Feel free to inquire for more details on solutions)

PP 25.23: Do any or all:

  1. Facing east, you make an about-face, and then you turn left.  You make another about-face, and turn left again.  Which direction is on your left side? South.
  2. A student in Mr. Smith’s Math 101 class spent 20 more minutes in class not paying attention then she did paying attention.  If the class is 52 minutes long, how long was the student inattentive? 32 minutes.
  3. Harry has 3 sisters and 5 brothers.  His sister Harriet has S sisters and B brothers.  What is the product of S & B? Harriet has 2 sisters and 6 brothers, so 2 * 6 = 12.
  4. What is the units digit of the smallest whole number greater than 1000 whose digits are all different? 3.

PP 25.22: Do any or all:

  1. (Suggested by Christine Porter, in honor of the season) What’s a math-type’s favorite Thanksgiving dessert? Pumpkin Pi(e)
  2. I am a proper fraction. The sum of my numerator and denominator is 60, and their difference is 10. What is my simplest name? 5/7 (Reduced from 25/35, meeting original conditions.)
  3. Fred set out to shop. He bought a present for $5, then spent half his remaining on some sandals, then bought lunch for $2, and finally spent half of his remaining money on a puzzle. He had $10 left at the end. How much did he have when he set out from home? $49 (Humorous Bonus: Given these prices, how old must this Puzzler be? LOL Pretty stinkin’ old!)
  4. The product of a set of distinct positive integers is 84. What is the least possible sum of those integers? If one assumes only 2 integers, the answer is 19 (7 & 12). If not (and the problem didn’t require it), then the answer would be 14 (2,2,3,& 7).

PP 25.20 & 25.21: Do any or all:

  1. (Suggested by Christine Porter, in honor of ourrecent house guest) What kind of snake is good at arithmetic? An adder.
  2. A woman perishes of old age on her 25th birthday. How can this happen? If she was born on Feb 29, she would only have a ‘real birthday’ every 4 years, so could have died (at age 100) on her 25th ‘birthday’.
  3. How many numbers less than 124 are divisible by 2,3,5,6,and 10? FOUR (30, 60, 90, and 120).
  4. Two different prime numbers are selected from the first 4 primes. What’s the probability that the sum of those two primes is even? 3/6 = 1/2. (Primes are 2,3,5,7. Sums are 5,7,8,9,10,12.)
  5. Which is bigger (area-wise): A square of side 2 or a circle with radius 2? The circle. (Square area is 4. Circle’s is 4*PI) (I wonder if I meant to say diameter?)

SPECIAL BONUS:Despite the fact that I forgot to post the link to the Puzzlers in the last Mailing, Jenni Wall was able to locate them. How could she have done this? I had a couple of clever (workable) answers here. What Jenni did was to find an old Mailing and checked the Puzzlers, which the system had already updated.

PP 25.19: Do any or all:

  1. You can find it in Mercury, Earth, Mars, Jupiter and Saturn, but not in Venus or Neptune. What is it? The letter r.
  2. How many rats are in a room if there is a rat in each of the four corners, three rats across from each rat, and a rat in the corner next to every rat? Four – one in each corner.
  3. A triangle’s hypotenuse is 13 units. One of the legs is 12.  What is the triangle’s area? 30 (sq. units)
  4. Divide 30 by 1/3 and add 10. What’s the result? 100

PP 25.18: Do any or all:

  1. True or False? Every month of the year has at least one day of the week that occurs five times that month. Elaboration preferred. It’s false, as stated but only because of (non leap-year) Februarys. Consider the 1st of every other month, for example. Whatever day that falls on will have dates of the 1st, 8th, 15th, 22nd, and 29th.
  2. Consider two statements: A) Every year has at least one Friday 13th. B) The longest period of time without a Friday 13th is 14 months. At least one of those statements is true. Is it possible for BOTH statements to be true? YES. Indeed, they are both true. (It turns out that the only possible 14 month intervals involve summer months around August).
  3. (Repeat – do you remember the answer?). Consider the spellings of all the whole numbers, starting at ONE. How long will you go before seeing the letter a? One thousand.
  4. (Geography repeat, for fun). Which two states are tied for having the most states they share a border with? Missouri and Tennesee each border on 8 other states.

PP 25.17: Do any or all:

  1. Riddle me this: What word contains 26 letters, but only has 3 syllables? Alphabet
  2. (Suggested by Christine Porter) When can you add 2 to 11 and get 1? Add two hours to 11:00 and you get 1:00.
  3. Al, Joe, Carl, and Dave were standing in line.  Dave was not first, Joe was between Al and Carl.  Al was between Dave and Joe.  In what order were they standing? Carl, Joe, Al, and Dave.
  4. If you bought an item for $63 and paid cash (US legal tender), using only six bills, BUT USED NO ONES, what were the bills? One $50 bill, one $5 bill, and four $2 bills

PP 25.16: Do any or all:

  1. (Another old classic? Suggested by Christine Porter) When is a door not a door? When it’s ajar.
  2. True or False? It is against the law to bury a person in Utah who is permanently living in Nevada. Statute or not, it’s not in good taste to bury a LIVING person (in any state!)
  3. Broadway is parallel to Campbell St. 44th St is perpendicular to Denver street. Denver is parallel to Campbell. Is 44th parallel or perpendicular to Broadway? Perpendicular
  4. Find the GCD (greatest common divisor) and the LCM (least common multiple) of 21 and 49. (Bonus: Notice anything?) GCD = 7, LCM = 147. (Several fun things were ‘noticed’ – all were true. Another thing to notice: 21 * 49 also equals 7 * 147. (And that’s always true: Given integers a & b, it it true that a*b = GCD*LCM of a & b.)

PP 25.15: Do any or all:

  1. (An old classic?) Jeff is camping outside Bemidji, MN with only oil lamps, a candle and some birch bark. He has only one match. Which should he light first? The match!
  2. If you could spend $50/minute, how long would it take you to spend one million dollars? 1 week, 6 days, 21 hours, 20 seconds.
  3. What is the next number in the sequence 3600, 1800, 600, 150, _30___?  (Divide by 2, then 3, then 4, then 5.)
  4. An auditorium has 4 doors. In how many ways is it possible to enter by one door and leave by another? 12

PP 25.14: Do any or all:

  1. (Idea suggested by Christine Porter.) Turn me on my side and I am everything. Cut me in half and I am nothing.  What am I? The number 8.
  2. Which 3 letters can be arranged to describe a dirty substance, a dirty animal, and an activity that can lead to dirty hands? A,R,T. (Tar, Rat, Art)
  3. Find the area of a square with perimeter 8.  Perimeter 8 –> Side 2 –> Area of 4.
  4. Two dice are to be rolled. Here are three possible outcomes: A) The number 7 is rolled. B) “Doubles” are rolled. C) Both dice have even numbers. Arrange those possibilities in order of greatest to least likely. C (9/36), A (7/36), B (6/36)

PP 25.13: Do any or all:

  1. A date on the calendar is a ‘twin prime day’, if both the month and day are primes. Lots of examples: 11/19, 7/23, 5/13, 2/7, etc. Interestingly, there is a twin prime date that does NOT occur every year! Which date would that be?Feb 29 (2/29)
  2. (Idea suggested by Christine Porter) Remember our friend Peter Piper from last time? Remember the age-old tongue twister about him? (Peter Piper picked a peck of pickled peppers . . . .). Here’s an interesting take I’d never thought about concerning the final question in that teaser: How many pickled peppers did PP pick? (Multiple answers possible?) All these years of saying this and I never thought about this fact: You can’t really PICK pickled peppers. (You have to pick the peppers before you can pickle the peppers.) So I’m going with the answer: NONE.
  3. In what state capitals will you find these guys: Harris, Sal, Jeff, and Al? (Pennsylvania – HARRISburg; Oregon – SALem; Missouri – JEFFerson City; and New York – ALbany.)
  4. For the sake of this problem, let’s arbitrarily assume that the average number of miles traveled by a car is 9000 miles/year. Approximately, how many gallons of gasoline could be saved in one year by a fuel-efficient car getting 32 mpg over a car getting 20 mpg? Roughly 169 gallons.

PP 25.12: Do any or all:

  1. It was a slow day for Peter Piper the Pickle Salesman. But after he sold half his pickles plus half a pickle he was left with one whole pickle. How many pickles did PP start with? 3 pickles
  2. (Submitted by Amy Ragsdale) One brother says to his younger brother, “Two years ago, I was three times as old as you were. In three years from now,I will be twice as old as you.”  How old are they each now? Younger brother is 7, older is 17.
  3. In a strange room, there are 6 rugs, and upon each rug are 6 six-legged tables. On each table are 6 six-legged creatures. What is the total number of creature legs in this silly story? (How about the total number of all legs?) There’s some ambiguity here about ‘legs’ (table legs and creature legs), and I’m not sure my attempts to clarify helped much. Other answers are possible, but I would have said 1776 ‘creature legs’ and 7776 total number of legs.
  4. An x by (x+10) rectangle is similar to an 11 by 16 rectangle. What is the perimeter of the smaller triangle? The 11 x 16 is similar to a 22 x 32 table of required dimensions. This makes the 11 x 16 the smaller of the two and its perimeter is 54.

PP 25.11: Do any or all:

  1. (Submitted by Christine Porter.) I can go all around the world but never leave my corner. What am I? A stamp.
  2. Erin left New York and flew to Los Angeles. The flight took 5 hours. If Erin left at 11:00 AM, when did she arrive? 1 PM, LA time.
  3. Batty Benny has a bizarre book. The foreword comes after the epilogue. The end is in the first half and the index is placed before the introduction. Maybe you have this book, too. What is it? Dictionary
  4. Three fathers – Pete, John, and Nick – have among them a total of 15 children of which 9 are boys. Pete has 3 girls and John has the same number of boys. John has 1 more child than Pete, who has 4 children. Nick has 4 more boys than girls and the same number of girls as Pete has boys. How many boys each do Nick and Pete have? Nick has 5, Pete has 1.
    • 4.5 Extra challenge: The problem above can be solved without the next-to-last sentence (“Nick has . . .”). Try solving it without that sentence. After the first two sentences of the puzzle, you can deduce all the info for Pete & John. Knowing the total # of Boys/Girls, you can deduce Pete’s complete info w/out the last sentence.
  5. ONGOING – Can’t Miss Fun!! Find your own Puzzler(s), Brain Teaser(s), Riddle(s), etc. Then submit it/them with the answers and you’ll get credit for this Puzzler! (And, if I use yours here in the future, you’ll be acknowledged.)

PP 25.10: Do any or all:

  1. Sometimes I’m green, sometimes I’m black. When I’m yellow, I’m a very nice fellow. That’s when I’m feeling mighty ‘a-peeling’. What am I? A Banana
  2. Mork can paint a room in 6 hours. Mindy can paint the same room in 3 hours. How long will it take if the work together? (I used to hate these problems. This one isn’t too bad.) 2 hours.
  3. The ratio of girls to boys in a class is 5:3. There are 6 boys in the class. How many students total in the class? 16
  4. Four cars come to a four-way stop, all coming from a different direction. They can’t decide who got there first, so they all proceed at the same time. They do not crash into each other, but all four cars go safely on their way. How is this possible? They all 4 make a right turn.
  5. Can’t Miss Fun!! Wild & Crazy time – saddle up. Find your own Puzzler(s), Brain Teaser(s), Riddle(s), etc. Then submit it/them with the answers and you’ll get credit for this Puzzler! (And, if I use yours here in the future, you’ll be acknowledged.)

PP 25.9: Do any or all:

  1. (Another old one?) Three guys go into a hardware store, all looking to buy the same thing. Moe buys 1 for $1. Curly buys 99 for $2. And Larry buys 628 for $3. What were they buying? House numbers.
  2. Two boxers are in a match scheduled for 12 rounds. (Pure boxing only – no kicking, UFC takedowns, or anything else). One of the boxers gets knocked out after only six rounds, yet no man throws a punch. How is this possible? It’s a women’s boxing match.
  3. Find the smallest positive integer which leaves a remainder of 1 when divided by 3, a remainder of 2 when divided by 4, and a remainder of 3 when divided by 5. 58
  4. There are six oranges in a box. Without cutting any of the oranges, divide them aoung six boys in such a way that one orange is left in the box. Give one of the boys his orange still in the box.
  5. (Semi-Bonus). Pick any two-digit number, square it and subtract 9. The result will never be prime. Can you explain why? (The number squared minus 9) is the ‘difference of two squares, so it factors into (the number +3) x (the number minus 3). A number with two other factors can’t be prime. (Bonus Bonus: Is the same result true for single digit integers? the way the question is phrased, YES. Slightly different wording produces a NO answer. )

PP 25.8: Do any or all:

  1. (An old one?) Fearless Freddy jumps out of a 68 story building without a parachute or safety equipment. Nevertheless he lands without injury. How does he do it? He jumps from the first floor.
  2. There are legitimately times and conditions when one can (seem to) go ‘back in time’. (Indeed, I’ve done it myself.) How can this happen? What I had in mind: Flying from New Zealand to Los Angeles non-stop can put you into LA at a local time that is earlier than the local time when you left. Rita Barger suggested: Every Fall at the daylight savings time change. I love it!
  3. a) An empty rectangular room measures 4 yards by 5 yards. How much would it cost to carpet this room with carpet that is on sale for $0.99 square foot? $178.20 b) What is the sale price of the carpet by the square yard? $8.91
  4. a) Find a fraction (not decimal) between 1/6 and 1/7. An infinite number of answers. 2/13 is one of them. b) Can you always find a fraction between two others? Yes. c) Can you always find more than one? Yes. NOTE: More information on both #4 and #5 in next Mailing’s Isn’t Math Wonderful?
  5. Sally was asked to find a fraction between 1/3 & 1/5, and notices she could add numerators and denominators get (1+1)/(3+5) = 2/8 = ¼, which is between 1/3 & 1/5.  Will that always work? Yes! If not, can you find a counter-example? 

PP 25.7: Do any or all:

  1. In which state would you be if you left St. Louis, went 5 miles east, then 200 miles north, then 50 miles west? Probably Iowa, but I took others. (I would also have taken ‘state of confusion’ :-))
  2. I start with the letter e. I end with the letter e. I usually contain one letter, but I am not the letter E. What am I? Envelope. (But I also got ‘eye’ and liked it.)
  3. Find the area of a square with perimeter 8. 4 square units.
  4. The radius of a circle is tripled. How does the area of the circle increase? The new area is multiplied by nine. (Ed Note: This is corrected. I had absently-mindedly and mistakenly typed ‘tripled’ earlier.)

PP 25.6: Do any or all:

  1. What starts today, can’t be found at noon, and is required to end sunset? The letter t.
  2. (A variation on an earlier Puzzler.) What’s the most money you can have and not be able to make exact change for a dollar? $1.19 (3Q, 4D, 4P)
  3. A can of tennis balls is exactly the right shape to hold 3 tennis balls stacked one upon another. Which is greater – the can’s height or its circumference? (Bonus points for explaining why.) The can’s circumference. (Height is 3 diameters, the circumference is (pi)diameters, and (pi) is greater than 3.
  4. A wooden cube is dropped into red paint. After drying, it is cut into 27 equally sized smaller cubes (like a Rubik’s cube). How many of those cubes are found to have red paint on . . . 4 faces? 0 3 faces? 8 2 faces? 12 1 face? 6 no faces? 1

PP 25.5: Do any or all:

  1. If 50 kids fit in a school bus, how many buses are needed to get 125 kids to a special event? Three buses.
  2. What’s the largest number of coins you can have and not be able to make exact change for a dollar? 99 – all pennies. (See another variation of this problem above.)
  3. On a certain day, I ate lunch at Tommy’s Cafe, took out 2 books from the library, visited the museum, and had a cavity filled. Tommy’s is closed on Wednesday, the library is closed on weekends, the museum is only open Monday, Wednesday, and Friday and my dentist has office hours Tuesday, Friday and Saturday. On which day of the week did I do all these things? Friday
  4. Each of the Bubba brothers has as many sisters as he has brothers, but each of the Bubba sisters has twice as many brothers as sisters. How many siblings are in the Bubba family? Seven siblings; 4 boys, three girls.

PP 25.4: Do any or all:

  1. Pi Day (3/14) Trivia: Pi Day is closely connected to two very famous physicists. One of them had a birthday on Pi Day, and the other died on Pi Day. Who were the two physicists? (Heavens, yes – feel free to use Google.) Albert Einstein was born on Pi Day (1879) and Stephen Hawking died on Pi Day (2018).
  2. Last week we celebrated Twin Primes Day on Mar 5. (3/5) When two odd primes are only two apart (like 3 & 5) they are called twin primes. There are only 3 twin prime days each year. What are the next two? May 7 (5/7) and Nov 13 (11/13).
  3. What word becomes plural when an ‘s’ is added, BUT becomes singular again when another ‘s’ is added? (Hint: Think royalty.) Prince. (Princes and Princess). I also took others that were very close.
  4. (An OLD classic!) A bottle and a cork together cost $1.10, and the bottle costs $1 more than the cork. How much does each item cost separately? Cork – $.05, Bottle – $1.05

PP 25.3: Do any or all:

  1. Their is six errers in this sentance. What are they? Their should be There. Is should be are. Sentance should be Sentence. Six should be five. (There are only 5 errors.)
  2. History time: There are three 2- or 3-generation sets of US Presidents. Can you name at least two of the pairs? The Adams (John, father; John Q, son); the Bushes (George, father; George W, son) and the Harrisons (William H, grandfather; Benjamin, grandson)
  3. The sum is 12, and the same digit is used 3 times to create that sum. But that digit is NOT a 4. What is it? 1. (11 + 1)
  4. (An easy repeat?) Homer’s mother has 4 children. Three of them are named Spring, Summer, and Autumn. What is the fourth child’s name? Homer

PP 25.2: Do any or all:

  1.  Ralph drives 60 miles at the speed of 30 mph. Then he returns on the same route, driving 60 mph. What was his average speed for the round trip? 40 mph. (120 miles in 3 hours.) (NOT 45 mph. You can’t average averages!)
  2. What number is 10 more than twice the number that is 10 more than 15 times (one-half of 10)? 180
  3. Guess The Next Three Letters In The Sequence GTNTL. ITS
  4. During which month do people sleep the least? February

PP 25.1: Do any or all:

  1.  The largest hailstone known to have fallen in the US fell in Coffeyville, KS, in Sept 1970.  It was 17.5 inches in circumference and weighed 1.67 pounds.  What was the approximate diameter of the hailstone? Approximately 5.57 inches.
  2. What is the smallest positive integer which is itself divisible by each of the integers from 1 to 12? 27720
  3. Your unorganized sock drawer contains 8 white socks, 8 blue socks, and 8 black socks. How many times do you need to reach inside the drawer and take out a sock at random to guarantee you have A)  a sock of each color? B) a pair of socks of the same color? A) 17 B) 4
  4. What was special about Jan 9 this year? (If you’re alert, you just might find this answer elsewhere in the Mailing. 🙂 ) Writing out the date – 1/9/25 – gives you the squares of the first 3 odd positive integers.
  5. The string of letters abcdefghijkmnopqrstuvwxyz could be said to represent a particular time of the year. What would that time be? Christmas. There is no letter l. (Noel)

Comments

One response to “Pesky Puzzlers 2025”

  1. Donald P Hayes

    #5. Christmas (noel – no L).