This is taken from Raymond Smullyan’s “The Riddle of Scheherazade” :“Iskandar wa

Question

This is taken from Raymond Smullyan’s “The Riddle of Scheherazade”

:“Iskandar was an extremely intelligent person who once asked his friend Kamar the ages in years of his three children. The following conversation ensued:

KAMAR: The product of their ages is thirty-six

ISKANDAR: That doesn’t tell me their ages.

KAMAR: Well, by coincidence, the sum of their ages is your own age.

ISKANDAR: (after several minutes of thought): I still don’t have enough information.

KAMAR: Well, if this will help, my son is more than a year older than both his sisters.

ISKANDAR: Oh good! Now I know their ages.

What are their ages?”

To get full points, you need to argue

1. That your answer does work with all the information given, and

2. That no other answer would satisfy all the information given – i.e. why does Iskandar believe that he knows their ages?

Explanation / Answer

Hi,
Here there are 3 conditions given, lets first list all possible combinations and drill down accoridngly
1. product is 36, since ages are integers, all possible tuples and their sums
1, 1, 36–38
1, 6, 6–13
1, 2, 18–21
2, 2, 9–13
1, 3, 12–16
2, 3, 6–11
1, 4, 9–14
3, 4, 3–10
2. sum of them is is ISKANDAR's age
the sum should be such that there are still multiple tuples, since he couldn't determine the ages, so the sum should be 13 as only that repeats for tuples  1, 6, 6 and 2, 2, 9
3.  son is more than a year older than both his sisters, means one value should be more than +1 of other 2 values, which means the ages are 2,2 and 9
two sisters are 2 and son is 9

Thumbs up if this was helpful, otherwise let me know in comments

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