Question 512613
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Assuming the ages of the three children are integers, then there are a finite set of possibilities.


1, 1, 36 (Sum 38)
1, 2, 18 (Sum 21)
1, 3, 12 (Sum 16)
1, 4, 9  (Sum 14)
1, 6, 6  (Sum 13)
2, 2, 9  (Sum 13)
2, 3, 6  (Sum 11)
3, 3, 4  (Sum 10)


Note that the sums are all unique except for 1, 6, 6 and 2, 2, 9.  So if it had been one of the other combinations, Sally would have known the ages when Bill told her it was the same as her house number.  But she didn't know, therefore the ages are either 1, 6, 6, or 2, 2, 9.  But knowing that the oldest has red hair means there IS an oldest, eliminating the 1, 6, 6 combination.  The children are 2, 2, and 9 years old.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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