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..."
Assuming that all the current ages are unique integers between 5 and 20, the following are all those whose combination of current sum and product are not unique:
--former-
-ages- sum prod sum prod
5 9 14 28 630 22 252
5 12 18 35 1080 29 480
5 14 16 35 1120 29 504
5 15 16 36 1200 30 546
6 7 15 28 630 22 260
6 9 20 35 1080 29 504
6 10 14 30 840 24 384
6 10 20 36 1200 30 576
6 12 14 32 1008 26 480
6 14 15 35 1260 29 624
6 15 16 37 1440 31 728
7 8 15 30 840 24 390
7 8 20 35 1120 29 540
7 9 16 32 1008 26 490
7 10 18 35 1260 29 640
8 9 20 37 1440 31 756
8 12 15 35 1440 29 780
8 15 18 41 2160 35 1248
9 10 16 35 1440 29 784
9 12 20 41 2160 35 1260
9 15 16 40 2160 34 1274
10 12 18 40 2160 34 1280
The following are those that are non-unique combination sum and product two years ago:
5 10 12 27 600 21 240
5 11 18 34 990 28 432
5 12 14 31 840 25 360
5 14 16 35 1120 29 504
6 7 14 27 588 21 240
6 8 17 31 816 25 360
6 8 20 34 960 28 432
6 9 20 35 1080 29 504
6 10 17 33 1020 27 480
6 11 12 29 792 23 360
6 12 16 34 1152 28 560
6 14 17 37 1428 31 720
7 8 14 29 784 23 360
7 8 18 33 1008 27 480
7 9 18 34 1134 28 560
7 10 20 37 1400 31 720
7 11 16 34 1232 28 630
8 9 17 34 1224 28 630
8 12 16 36 1536 30 840
8 14 16 38 1792 32 1008
8 16 17 41 2176 35 1260
9 10 17 36 1530 30 840
9 11 18 38 1782 32 1008
9 12 20 41 2160 35 1260
10 14 17 41 2380 35 1440
11 12 18 41 2376 35 1440
11 17 18 46 3366 40 2160
12 14 20 46 3360 40 2160
Only 6 9 20 appears on both lists, and is the set of ages.
|
|
Posted by Charlie
on 2005-03-03 20:47:33 |
solution
