Puzzler

The Census Conundrum

During a recent census, a man was being interviewed by a census taker. He told the census taker that he had 3 children. When asked their ages, the man replied, "The product of their ages is 72. The sum of their ages is the same as the number on my mailbox."

The census taker ran to the mailbox and checked the number. "I still can't tell," he said. The man replied, "Oh sorry. I have to go. My oldest is sick in bed."

With that, the census taker wrote down the ages of the 3 children and left.

How old are the children?

Solution

The census taker knows the sum of the children's ages by looking at the number on the mailbox. That still leaves multiple possibilities.

Considering the product of their ages is 72, it must be one of these:

1,1,72
1,2,36
1,3,24
1,4,18
1,6,12
1,8,9
2,2,18
2,3,12
2,4,9
2,6,6
3,3,8
3,4,6

We can rule out the first three cases because children can't be 24, 36 or 72 years old.

Because the census taker knew the total (from the number on the mailbox) but said that he had insufficient information to give a definitive answer, there must be more than one solution with the same total. Since the sum of their ages is the same as the number on the mailbox, find all the possible sums. possible sums.

1+1+72 = 74
1+2+36 = 39
1+3+24 = 28
1+4+18 = 23
1+6+12 = 19
1+8+9 = 18
2+2+18 = 22
2+3+12 = 17
2+4+9 = 15
2+6+6 = 14
3+3+8 = 14
3+4+6 = 13

The number 14 is the only sum that occurs more than once in the list. This narrows it down to two possibilities:

2, 6, and 6
3, 3, and 8

Is it an OLDER set of twins or a YOUNGER set of twins?

Remember, the man disclosed that his oldest child was ill. The fact that he was sick had nothing to do with it, but the fact that there is an OLDEST child does. It rules out the case of their ages being 2, 6, and 6 for then the oldest two would be twins and neither would be the OLDEST.

Now you know that their ages are 3, 3, and 8.