## Monday, July 28, 2008

### Insurance Agents are Quick on Their Feet

A mathematician sits down to talk to his insurance agent. The agent, after answering some preliminary questions, the mathematician gets bored and tries to play a game. When the agent asks him how many children he has, the mathematician replies "3."

"And what are their ages?"

"The product of their ages is equal to 36," said the mathematician.

"Sir, that's not enough information."

"Well then, the sum of their ages is equal to the number of shops in front of your office," the mathematician spoke, now thoroughly enjoying himself.

"Again sir, that just isn't enough information," the agent replied.

"My oldest child likes knowing that she is the oldest."

"Thank you, sir, that's enough information. Shall we move on to the next set of questions?"

How did the agent figure out how old the children were?

1. Perhaps the insurance agent had 13 shops in front of his office. This means that, with the first two clues, there were two possible combinations (9,2,2 and 6,6,1). When he said his oldest child likes knowing "she" (singular) is oldest, he knows that it has to be 9,2,2.

2. 2, 2, 9. All other combinations are unique.

4. If the product of their 3 ages is 36, the possible answers are as follows (the sum of the three numbers is in parentheses):
1,1,36 (38)
1,2,18 (21)
1,3,12 (16)
1,4,9 (14)
1,6,6 (13)
2,2,9 (13)
2,3,6 (11)
3,3,4 (10)

Now if the agent knew the number of stores in front was 38, he would have known the answer immediately after the second response. Since he didn't have enough information, the number of storefronts was 13, the only non-unique answer.

The two possible answers at this point are:
1,6,6
2,2,9

But when he found out the oldest was singular, he knew the answer had to be 2, 2, and 9.

BTW, I believe you can make an argument about that last bit of reasoning, but that's what I'm going to stick with.

5. when twins are born they are not born at the exact same time. with all of the twins that I know one twin likes to make it abundantly clear that he/she is the oldest. even if it is only by minutes or hours. so being older is often more important to the older twin than it would be to an older sibling

6. You've pointed out the real flaw in this puzzle. But I just couldn't think of a better way to hint that the first wasn't a twin.

Any ideas on how to re-write it?

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