Brain Teasers – May/June ’17

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?
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?
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?
4. Find three consecutive odd integers which are all prime.
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?
6.  If x#y = x + y +7, then what is the value of (2#3) # (7#0)?
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?
8. My neighbor has four daughters and each daughter has exactly one brother.  How many children does my neighbor have?
9. What is the largest integer you can square and get an answer less than 3000?
10. 1/19 is to 1/17 as what number is to 95?
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?
12. Simplify this expression:  (99 – 9) x (99 – 19) x (99 – 29) x . . . x (99 – 199).
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?
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 nigth, he slides down 3 ft.  How many days will it take him to jump out of the well?
15. “Brothers and sisters have I none, but this man’s father is my father’s son.”  To whom is the speaker referring?

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.) 
B2.  (see #4 above.)  It turns out there is only one solution to #4 above.  Why is that?
B3.  (see #6 above.)  If x&y = x # (y+7), then what is the value of (2#3) & (7#0)?
B4.  (see #9 above.)  Suppose we do not insist on an integer in #9 above.  How (if any) does that change the answer?