Talk:Puzzles/Arithmetical puzzles/Three Daughters

Clue 1 - product of ages is 36: Ages must be one of
 * 36, 1, 1 (although this is pretty unlikely)
 * 18, 2, 1
 * 12, 3, 1
 * 9, 4, 1
 * 9, 2, 2
 * 6, 3, 2
 * 4, 3, 3

Am I missing any?

Clue 2 - sum of ages is same as number of my house
 * 36 + 1 + 1 = 38
 * 18 + 2 + 1 = 21
 * 12 + 3 + 1 = 16


 * 9 + 4 + 1 = 14
 * 9 + 2 + 2 = 13
 * 6 + 3 + 2 = 11
 * 4 + 3 + 3 = 10

Since the salesman knows the number of the house, he should be able to work it out. If two of the sums were the same, and one of them had the largest two ages the same, then the third clue (My eldest daughter plays piano) would confirm that it was the other one.

So what is wrong with my math? I have missed something otherwise I would need clue 3. Nanobug 20:54, 10 Oct 2003 (UTC)


 * In the paragraph "since the salesman..." you have analyzed the situation perfectly! You are indeed missing one combination (hint: it adds up to 13) Thomas

The missing combination is 1, 6, 6. Combining with Nanobug's work above, the complete solution is:

Clue 1: Product is 36.

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Find all combinations with product 36:


 * 1, 1, 36
 * 1, 2, 18
 * 1, 3, 12
 * 1, 4, 9
 * 1, 6, 6
 * 2, 2, 9
 * 2, 3, 6
 * 3, 3, 4

Clue 2: Sum is house number.

Sums are:


 * 1 + 1 + 36 = 38
 * 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

Clue 3: Eldest plays piano.

Presumably, this means there is no tie for oldest age. (Since the ages are only given to the year, it is possible for two to have the same age but one be elder than the other. Interpeted this way the clue tells us nothing. But the salesman derived pertinant information from it, so we must also.)

Now the salesman knows the housenumber (though we don't). Thus if the house number is other than 13, the salesman would have been able to figure out the answer after clue 2. So the number is 13. (I guess we know it after all :-). By clue three we eliminate 1, 6, 6. So the ages of the daughters are


 * 2, 2, and 9

Eric119 03:17, 11 Oct 2003 (UTC)


 * That's right. nice job, Eric! Thomas


 * Duh! Of course! Nanobug 20:37, 13 Oct 2003 (UTC)