Tom meets a new neighbour, Cheryl, next door to him. During the conversation with Cheryl, Tom asks her: “How many kids do you have”. “Three” replied Cheryl. Tom asked “How old are they?”
Cheryl answered:”The product of their ages is 36. The sum of their ages are the same as my house number.” After some time Tom replied “I can’t figure it out. I don’t have enough information”. “My apologies, I forgot to tell you that my youngest child likes strawberry milk” replied Cheryl. Tom figured out their ages after her answer and Cheryl confirmed that he was right.
How old are Cheryl’s children?
The children are 1, 6 and 6 years old.
The product of their ages is 36, so none of them can be older than 36. The number 36 has to be expressed as the product of 3 numbers. Their possible ages are (The sum of their ages is in brackets):
1, 1, 36 (3938)
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)
Since Cheryl is Tom’s next door neighbour, Tom knows Cheryl’s house number. Tom would know the children’s ages in every case that sums up to a unique number except for the sum of 13, which have 2 combinations of possible ages.
As a result, Tom would be confused as he has to pick between the 2 combinations: (1,6,6) and (2,2,9). Cheryl then tells Tom about her youngest child who likes strawberry milk which tells Tom that there is only 1 youngest child.