Analytical Puzzle Problem

This analytical puzzle involves a census worker asking a mother for the ages of her three children. We are told that the product of the children’s ages is 36, and the sum of their ages is the same as the address of the house to the north. After being given this limited information, the census worker looks at the address next door, and returns to ask the mother for more information. The mother simply tells the census worker that the oldest child is sleeping upstairs.

Analysis The first step in solving this problem is to determine the factors of 36 (using 3 numbers) in order to further examine the riddle. These factors, followed by their sum, are as follows: Solution When looking at the possibilities, we only see two options which would have the same house number. This must be the case, since the census worker returned to ask an additional question. This solves the house number question. The direction of the placement of the house (“to the north”) is unnecessary information.

The house number must be 13, leaving only two possibilities of factors: 1, 6, and 6; and 2, 2, and 9. However, since the census worker asked for additional information, and the answer was enough to satisfy him without further questions, we must surmise the correct answer is 2, 2, and 9. If the answer had been 1, 6, and 6, the mother would have said “the twins are sleeping upstairs” rather than simply “the oldest is sleeping upstairs”. Therefore, I surmise that the ages of the children are 2, 2, and 9, and the house number of the home next door to the north is 13.