Riddle Me This: SOLUTIONS

The following three riddles are reprinted from Fundrum My Conundrum (A Book of Riddles), by Ben Kovler ’00 and Ray Epstein. Published by Fundrum Publishing, the book of 100 puzzles, ranging from novice to deadly, is available through the Website, www.fundrum.com. (The number following each puzzle is the riddle’s number in the book.) Click here to return to the puzzler.

1. A prisoner is told, “If you tell a lie we will hang you; if you tell the truth we will shoot you.” What statement can he make about the situation to save himself? (#5)

1. The prisoner says “You are going to hang me.” They can’t hang him because that would mean he didn’t lie. They can’t shoot him because that would mean he didn’t tell the truth.

2. Eight BBs look alike but one is slightly heavier than the others. How can you identify the heavy BB in only two weighings on a balance scale? (#68)

2. Weigh three BBs on each side. If one side goes down it must contain the heavy BB. Weigh two of those, one on each side, and if one side goes down, it must contain the heavy BB. If they balance, then the one you did not weigh is the heavy BB. If, on the first weighing, the scale balances, then you have two BBs left. Place one on each side. The heavy one will go down.

3. Two mathematicians are walking down the street. The first says to the second, “I know you have three sons. What are their ages?” The second replies, “The product of their ages is 36.” The first says, “I can’t tell their ages from that.” The second says, “Well, the sum of their ages is the same as that address across the street.” The first says, “I still can’t tell.” The second says, “The oldest is visiting his grandfather today.” The first says, “Now I know their ages.” Do you? (#98)

3. Their ages are 2, 2 and 9. There are only eight combinations of three numbers that multiply out to 36 (1X1X36; 1X6X6; 1X2X18; 1X3X12; 1X4X9; 2X2X9; 2X3X6; and 3X3X4). Six of their sums are unique, so if it were one of those, the first mathematician would recognize the number across the street that matches and he would know the answer, but he doesn’t. Two combinations (1X6X6 and 2X2X9) result in the same sum, so he can’t know which is correct. Upon hearing that there is an “oldest” he sees that only one of the two sums qualifies, because the other doesn’t have an oldest child.