Solution to Problem 78

Congratulations to this week's winners

Courtney Pelowski, Mike Dewitt, Shaun Lewis, Ray Kremer

Scott Peters also submitted a correct solution. Correct solutions were also submitted by Ron Welch, Yan Fridman, Aaron Kahn, Tim Kelly, Bill Webb, Cyril Terakopiantz, Steve Prowse, Emanuele Macri, Loranzo Pozzoli, Matt Humbard, Greg Paul, Philippe Fondanaiche, Dane Brooke.

Since the product of the ages is 72, the ages must be among the factors of 72. This gives the following possibilitites.

First Age	Second Age	Third Age	Sum of Ages
1	1	72	74
1	2	36	39
1	3	24	28
1	4	18	23
1	6	12	19
1	8	9	18
2	2	18	22
2	3	12	17
2	4	9	15
2	6	6	14
3	3	8	14
3	6	4	13

Since knowing the sum of the ages did not uniquely identify the ages of the nieces, you must conclude that the sum of the ages is 14, as no other sum appears more than once. The final information about the likes of the eldest niece tells the neighbor that there is an eldest niece, which would not be the case if the nieces ages were 2, 6 and 6. The only remaining possibility is that the nieces are 3, 3 and 8, and that incidentally, the house number is 14.

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Page last updated 13 January 2000.