May/Jun17 BTs – Solutions, Solvers, Etc.

May/June17 Brain Teasers – SUMMARY

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

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! Rita Barger, Jim Waterman, Amy Ragsdale, Anita Dixon, Alexis Avis, Jennifer Steele.
2.  A man tossed a baseball 20 feet.  It stopped in mid-air, reversed directions and came back to him.  How can this be explained? He threw it straight up. Rita Barger, Jim Waterman, Amy Ragsdale, Christine Porter, Anita Dixon, Alexis Avis, Jennifer Steele.
3. [An old classic!] A brick weighs 3 pounds plus half (the weight of) a brick.  How much does a brick and a half weigh?  Nine (9) pounds.  Rita Barger, Jim Waterman, Amy Ragsdale, Anita Dixon, Alexis Avis
4. Find three consecutive odd integers which are all prime. 3,5,7.  Rita Barger, Jim Waterman, Amy Ragsdale, Anita Dixon, Alexis Avis
5.  You have a string of 10 consecutive integers.  The sum of the first three is 39.  What is the sum of the last 3?  60. Rita Barger, Amy Ragsdale, Anita Dixon, Alexis Avis
6.  If x#y = x + y +7, then what is the value of (2#3) # (7#0)?  33 Rita Barger, Amy Ragsdale, Anita Dixon
7.  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. Rita Barger, Jim Waterman, Amy Ragsdale, Anita Dixon, Alexis Avis, Jennifer Steele.
8. My neighbor has four daughters and each daughter has exactly one brother.  How many children does my neighbor have? Five (5). Rita Barger, Jim Waterman, Amy Ragsdale, Anita Dixon, Alexis Avis, Jennifer Steele.
9. What is the largest integer you can square and get an answer less than 3000?  54. Rita Barger, Amy Ragsdale, Anita Dixon, Alexis Avis
10. 1/19 is to 1/17 as what number is to 95? 85  Rita Barger, Amy Ragsdale, Anita Dixon, Alexis Avis
11. In the first quarter of a game, the Denver Nuggets missed only 7 of their 25 field goal attempts.  What was their scoring percentage for that quarter? 72%. Rita Barger, Amy Ragsdale,, Alexis Avis
12. Simplify this expression:  (99 – 9) x (99 – 19) x (99 – 29) x . . . x (99 – 199). Zero (0).  Rita Barger,  Alexis Avis
13. In my hand, I have two US coins whose total value is 55 cents, but one of the coins is not a nickel.  What are the two coins? A half dollar and a nickel.  (One of them is not a nickel.)  Rita Barger, Jennifer Steele
14. A frog is at the bottom of a 30-foot well.  Each day he is able to jump up 5 ft, but during the night, he slides down 3 ft.  How many days will it take him to jump out of the well?  14 days. (On the 14th day, he gets out before sliding back down.)   Rita Barger, Alexis Avis, Jennifer Steele
15. “Brothers and sisters have I none, but this man’s father is my father’s son.”  To whom is the speaker referring? He is referring to his son. Alexis Avis

BONUSES

B1.   Counterfeit Coin #4  Another new twist of Jan/Feb’s problems.  I am now convinced this problem can be solved with up to 27 coins(!).   So pick your own number(s) and solve:  You know one of them is counterfeit – and that it is slightly heavier than the good coins, and you still have your balance scale. Determine the bad coin, still with only 3 weighings.  (A ‘weighing’ consists of coins being placed on both sides.) No solutions submitted again.  May or may not continue on to next time.  (For details of solutions, ask.)
B2.  (see #4 above.)  It turns out there is only one solution to #4 above.  Why is that? Any other collection of consecutive odd integers contains a multiple of 3. [Note that the 3 in 3,5,7 is multiple of 3, but in this case it’s also prime.] (For further clarification, ask.)  Anita Dixon (with partial credit to Jim Waterman.)
B3.  (see #6 above.)  If x&y = x # (y+7), then what is the value of (2#3) & (7#0)? 33. Rita Barger, Anita Dixon.
B4.  (see #9 above.)  Suppose we do not insist on an integer in #9 above.  How (if any) does that change the answer? Considerably!  There is NO such number. [The square root of 3000 is 7.34846 . . . and there are always decimals less than that but larger than anything picked earlier.]  Rita Barger, Anita Dixon (with partial credit to Amy Ragsdale.)