Here are a couple of age puzzles from David Pleacher’s great site. Answers are on there too.
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During a recent census, a man told the census taker that he had 3 children.
When asked their ages, he replied, “The product of their ages is 72.”
“The sum of their ages is the same as my house number.”
The census taker ran to the door and looked at the house number.
“I still can’t tell,” she complained.
“Oh, that’s right. I forgot to tell you that the oldest one likes apple pie.”
The census taker promptly wrote down the ages of the three children.
How old are they?
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Edie and Dave were talking when they saw three people coming toward them.
“I wonder how old they are,” said Edie.
Dave replied, “I know them!
The product of their ages is 2,450 and the sum of their ages is twice your age.”
“That’s all well and good,” said Edie, “but I need more information.”
“Oh yes,” said Dave.
“Well, I am older than any of the three.”
“Now, I can figure their ages,” said Edie.
How old are the three?
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In case they were too easy here is a fiendish one to try by John H. Conway.
Last night I sat behind two wizards on a bus, and overheard the following: A: “I have a positive integral number of children, whose ages are positive integers, the sum of which is the number of this bus, while the product is my own age.” B: “How interesting! Perhaps if you told me your age and the number of your children, I could work out their individual ages?” A: “No.” B: “Aha! AT LAST I know how old you are!” Now what was the number of the bus?
Here is a paper which discusses the puzzle and solution.