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Vandaag is het 18 December 2017

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Insurance company - logic puzzle

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A man would like to take a new health insurance. An officer taking care of these matters says to the man: "Please tell me how many children you have." The man answers: "I have three of them." The officer: "What are the ages of your children?". The man answers: "The product of the ages is equal to 36." The officer replies: "This is not enough information Sir!". "Sorry that I was a little bit unclear, but the sum of the ages is equal to the number of shops in front of your office," says the man. The officer: "This still isn't enough information Sir!". The man replies: "My oldest child loves chocolate." The officer: "Thanks for your cooperation, I now know the ages."
Are you as smart as the officer? Then give the ages of the children.

Explanation

The product of the ages is 36. Using this one can make the following combination of ages:

1,36, 1 sum = 38
1,18, 2 sum = 22
1,12, 3 sum = 16
1, 9, 4 sum = 14
1, 6, 6 sum = 13
2, 9, 2 sum = 13
2, 6, 3 sum = 11
3, 3, 4 sum = 10

After the man had said that the product of the ages is equal to 36, the officer didn't have enough information. Then he was told that the sum is equal to number of shops in front of the office. He replied by saying that this still isn't enough information. So the sum of the ages should be 13, because otherwise he would have known the ages immediately. The last statement is that that the oldest child loves chocolate. So there is an oldest child. Hence the officer concludes that the ages of the children are 2, 2 and 9 years.