The hostess, at her 20th wedding anniversary party, tells you that her youngest child likes her to pose this problem to guests, and she proceeds to explain: "I normally ask guests to determine the ages of my three children, given the sum and products of their ages. Since Smith gave an incorrect answer to the problem tonight and Jones gave an incorrect answer at the party two years ago, I'll let you off the hook."

Your response is "No need to tell me more, their ages are..."

(In reply to re(3): Solution (??) by Charlie)

I rewrote the program from scratch, and allowed for duplicate current ages, due to the under-1-year gestation period.  I allowed a minimum age of 5 now (3 two years ago, to allow for addition and multiplication abilities), maximum age 19 now, to avoid shotgun weddings.

Those with ambiguous current ages are:

cur ages sum prod
 5  8  9 22  360 16  126
 5  9 14 28  630 22  252
 5 12 12 29  720 23  300
 6  6 10 22  360 16  128
 6  7 15 28  630 22  260
 6  8 15 29  720 23  312
 6 10 14 30  840 24  384
 6 12 14 32 1008 26  480
 6 12 16 34 1152 28  560 *
 6 14 15 35 1260 29  624
 7  8 15 30  840 24  390
 7  9 16 32 1008 26  490
 7 10 18 35 1260 29  640
 7 12 12 31 1008 25  500
 8  8 18 34 1152 28  576 *
 8  9 14 31 1008 25  504
 8 12 15 35 1440 29  780
 8 15 15 38 1800 32 1014
 9 10 16 35 1440 29  784
 9 15 16 40 2160 34 1274
10 10 18 38 1800 32 1024
10 12 18 40 2160 34 1280

Those with ambiguous ages 3 years ago are

cur ages         sum prod
 5  8 10 23  400 17  144
 5 10 12 27  600 21  240
 5 12 14 31  840 25  360
 6  6 11 23  396 17  144
 6  7 14 27  588 21  240
 6  8 17 31  816 25  360
 6 10 17 33 1020 27  480
 6 11 12 29  792 23  360
 6 12 16 34 1152 28  560 *
 6 14 14 34 1176 28  576
 7  8 14 29  784 23  360
 7  8 18 33 1008 27  480
 7  9 18 34 1134 28  560 *
 7 10 11 28  770 22  360
 7 11 16 34 1232 28  630
 7 14 14 35 1372 29  720
 8  8 12 28  768 22  360
 8  8 18 34 1152 28  576
 8  9 17 34 1224 28  630
 8 10 17 35 1360 29  720
 8 12 16 36 1536 30  840
 8 14 16 38 1792 32 1008
 9 10 17 36 1530 30  840
 9 11 18 38 1782 32 1008
 9 14 14 37 1764 31 1008
10 11 16 37 1760 31 1008
10 14 17 41 2380 35 1440
11 12 18 41 2376 35 1440

The only set that appears on both lists is 6 12 16, marked with * above, along with the lines that make this ambiguous in the respective lists. In the case of current ages, that's 8, 8 and 18. But the mother actually did not have such a busy year 8 years ago, and again, has children 6, 12 and 16.

Posted by Charlie on 2005-03-04 18:47:53