A puzzle by Princeton mathematician John Horton Conway:
Last night I sat behind two wizards on a bus, and overheard the following:
A: I have a positive integral number of children, whose ages are positive integers, the sum of which is the number of this bus, while the product is my own age.
B: How interesting! Perhaps if you told me your age and the number of your children, I could work out their individual ages?
A: No.
B: Aha! AT LAST I know how old you are!
Rem: Taking in account the fatherhood limitations, this is uniquely solvable.
(In reply to
re: computer aided solution -- continued by Charlie)
25 46 2 2 23
25 48 8 1 1 1 1 1 1 3 16
25 51 7 1 1 1 1 1 3 17
25 54 6 1 1 1 1 3 18
25 56 9 1 1 1 1 1 1 1 4 14
25 57 5 1 1 1 3 19
25 60 4 1 1 3 20
25 60 8 1 1 1 1 1 1 4 15
25 60 9 1 1 1 1 1 1 2 2 15
25 63 3 1 3 21
25 64 7 1 1 1 1 1 4 16
25 64 8 1 1 1 1 1 2 2 16
25 65 9 1 1 1 1 1 1 1 5 13
25 66 2 3 22
25 68 6 1 1 1 1 4 17
25 68 7 1 1 1 1 2 2 17
25 70 8 1 1 1 1 1 1 5 14
25 72 5 1 1 1 4 18
25 72 6 1 1 1 2 2 18
25 72 9 1 1 1 1 1 1 1 6 12
25 75 7 1 1 1 1 1 5 15
25 76 4 1 1 4 19
25 76 5 1 1 2 2 19
25 77 9 1 1 1 1 1 1 1 7 11
25 78 8 1 1 1 1 1 1 6 13
25 80 3 1 4 20
25 80 4 1 2 2 20
25 80 6 1 1 1 1 5 16
25 80 9 1 1 1 1 1 1 1 8 10
25 81 9 1 1 1 1 1 1 1 9 9
25 84 2 4 21
25 84 3 2 2 21
25 84 7 1 1 1 1 1 6 14
25 84 8 1 1 1 1 1 1 7 12
25 84 9 1 1 1 1 1 1 2 3 14
25 85 5 1 1 1 5 17
25 88 8 1 1 1 1 1 1 8 11
25 90 4 1 1 5 18
25 90 6 1 1 1 1 6 15
25 90 8 1 1 1 1 1 1 9 10
25 90 8 1 1 1 1 1 2 3 15
25 91 7 1 1 1 1 1 7 13
25 95 3 1 5 19
25 96 5 1 1 1 6 16
25 96 7 1 1 1 1 1 8 12
25 96 7 1 1 1 1 2 3 16
25 98 6 1 1 1 1 7 14
25 99 7 1 1 1 1 1 9 11
26 34 9 1 1 1 1 1 1 1 2 17
26 36 8 1 1 1 1 1 1 2 18
26 38 7 1 1 1 1 1 2 19
26 40 6 1 1 1 1 2 20
26 42 5 1 1 1 2 21
26 44 4 1 1 2 22
26 46 3 1 2 23
26 48 2 2 24
26 48 9 1 1 1 1 1 1 1 3 16
26 51 8 1 1 1 1 1 1 3 17
26 54 7 1 1 1 1 1 3 18
26 57 6 1 1 1 1 3 19
26 60 5 1 1 1 3 20
26 60 9 1 1 1 1 1 1 1 4 15
26 63 4 1 1 3 21
26 64 8 1 1 1 1 1 1 4 16
26 64 9 1 1 1 1 1 1 2 2 16
26 66 3 1 3 22
26 68 7 1 1 1 1 1 4 17
26 68 8 1 1 1 1 1 2 2 17
26 69 2 3 23
26 70 9 1 1 1 1 1 1 1 5 14
26 72 6 1 1 1 1 4 18
26 72 7 1 1 1 1 2 2 18
26 75 8 1 1 1 1 1 1 5 15
26 76 5 1 1 1 4 19
26 76 6 1 1 1 2 2 19
26 78 9 1 1 1 1 1 1 1 6 13
26 80 4 1 1 4 20
26 80 5 1 1 2 2 20
26 80 7 1 1 1 1 1 5 16
26 84 3 1 4 21
26 84 4 1 2 2 21
26 84 8 1 1 1 1 1 1 6 14
26 84 9 1 1 1 1 1 1 1 7 12
26 85 6 1 1 1 1 5 17
26 88 2 4 22
26 88 3 2 2 22
26 88 9 1 1 1 1 1 1 1 8 11
26 90 5 1 1 1 5 18
26 90 7 1 1 1 1 1 6 15
26 90 9 1 1 1 1 1 1 1 9 10
26 90 9 1 1 1 1 1 1 2 3 15
26 91 8 1 1 1 1 1 1 7 13
26 95 4 1 1 5 19
26 96 6 1 1 1 1 6 16
26 96 8 1 1 1 1 1 1 8 12
26 96 8 1 1 1 1 1 2 3 16
26 98 7 1 1 1 1 1 7 14
26 99 8 1 1 1 1 1 1 9 11
27 36 9 1 1 1 1 1 1 1 2 18
27 38 8 1 1 1 1 1 1 2 19
27 40 7 1 1 1 1 1 2 20
27 42 6 1 1 1 1 2 21
27 44 5 1 1 1 2 22
27 46 4 1 1 2 23
27 48 3 1 2 24
27 50 2 2 25
27 51 9 1 1 1 1 1 1 1 3 17
27 54 8 1 1 1 1 1 1 3 18
27 57 7 1 1 1 1 1 3 19
27 60 6 1 1 1 1 3 20
27 63 5 1 1 1 3 21
27 64 9 1 1 1 1 1 1 1 4 16
27 66 4 1 1 3 22
27 68 8 1 1 1 1 1 1 4 17
27 68 9 1 1 1 1 1 1 2 2 17
27 69 3 1 3 23
27 72 2 3 24
27 72 7 1 1 1 1 1 4 18
27 72 8 1 1 1 1 1 2 2 18
27 75 9 1 1 1 1 1 1 1 5 15
27 76 6 1 1 1 1 4 19
27 76 7 1 1 1 1 2 2 19
27 80 5 1 1 1 4 20
27 80 6 1 1 1 2 2 20
27 80 8 1 1 1 1 1 1 5 16
27 84 4 1 1 4 21
27 84 5 1 1 2 2 21
27 84 9 1 1 1 1 1 1 1 6 14
27 85 7 1 1 1 1 1 5 17
27 88 3 1 4 22
27 88 4 1 2 2 22
27 90 6 1 1 1 1 5 18
27 90 8 1 1 1 1 1 1 6 15
27 91 9 1 1 1 1 1 1 1 7 13
27 92 2 4 23
27 92 3 2 2 23
27 95 5 1 1 1 5 19
27 96 7 1 1 1 1 1 6 16
27 96 9 1 1 1 1 1 1 1 8 12
27 96 9 1 1 1 1 1 1 2 3 16
27 98 8 1 1 1 1 1 1 7 14
27 99 9 1 1 1 1 1 1 1 9 11
28 38 9 1 1 1 1 1 1 1 2 19
28 40 8 1 1 1 1 1 1 2 20
28 42 7 1 1 1 1 1 2 21
28 44 6 1 1 1 1 2 22
28 46 5 1 1 1 2 23
28 48 4 1 1 2 24
28 50 3 1 2 25
28 54 9 1 1 1 1 1 1 1 3 18
28 57 8 1 1 1 1 1 1 3 19
28 60 7 1 1 1 1 1 3 20
28 63 6 1 1 1 1 3 21
28 66 5 1 1 1 3 22
28 68 9 1 1 1 1 1 1 1 4 17
28 69 4 1 1 3 23
28 72 3 1 3 24
28 72 8 1 1 1 1 1 1 4 18
28 72 9 1 1 1 1 1 1 2 2 18
28 75 2 3 25
28 76 7 1 1 1 1 1 4 19
28 76 8 1 1 1 1 1 2 2 19
28 80 6 1 1 1 1 4 20
28 80 7 1 1 1 1 2 2 20
28 80 9 1 1 1 1 1 1 1 5 16
28 84 5 1 1 1 4 21
28 84 6 1 1 1 2 2 21
28 85 8 1 1 1 1 1 1 5 17
28 88 4 1 1 4 22
28 88 5 1 1 2 2 22
28 90 7 1 1 1 1 1 5 18
28 90 9 1 1 1 1 1 1 1 6 15
28 92 3 1 4 23
28 92 4 1 2 2 23
28 95 6 1 1 1 1 5 19
28 96 2 4 24
28 96 3 2 2 24
28 96 8 1 1 1 1 1 1 6 16
28 98 9 1 1 1 1 1 1 1 7 14
29 40 9 1 1 1 1 1 1 1 2 20
29 42 8 1 1 1 1 1 1 2 21
29 44 7 1 1 1 1 1 2 22
29 46 6 1 1 1 1 2 23
29 48 5 1 1 1 2 24
29 50 4 1 1 2 25
29 57 9 1 1 1 1 1 1 1 3 19
29 60 8 1 1 1 1 1 1 3 20
29 63 7 1 1 1 1 1 3 21
29 66 6 1 1 1 1 3 22
29 69 5 1 1 1 3 23
29 72 4 1 1 3 24
29 72 9 1 1 1 1 1 1 1 4 18
29 75 3 1 3 25
29 76 8 1 1 1 1 1 1 4 19
29 76 9 1 1 1 1 1 1 2 2 19
29 80 7 1 1 1 1 1 4 20
29 80 8 1 1 1 1 1 2 2 20
29 84 6 1 1 1 1 4 21
29 84 7 1 1 1 1 2 2 21
29 85 9 1 1 1 1 1 1 1 5 17
29 88 5 1 1 1 4 22
29 88 6 1 1 1 2 2 22
29 90 8 1 1 1 1 1 1 5 18
29 92 4 1 1 4 23
29 92 5 1 1 2 2 23
29 95 7 1 1 1 1 1 5 19
29 96 3 1 4 24
29 96 4 1 2 2 24
29 96 9 1 1 1 1 1 1 1 6 16
30 42 9 1 1 1 1 1 1 1 2 21
30 44 8 1 1 1 1 1 1 2 22
30 46 7 1 1 1 1 1 2 23
30 48 6 1 1 1 1 2 24
30 50 5 1 1 1 2 25
30 60 9 1 1 1 1 1 1 1 3 20
30 63 8 1 1 1 1 1 1 3 21
30 66 7 1 1 1 1 1 3 22
30 69 6 1 1 1 1 3 23
30 72 5 1 1 1 3 24
30 75 4 1 1 3 25
30 76 9 1 1 1 1 1 1 1 4 19
30 80 8 1 1 1 1 1 1 4 20
30 80 9 1 1 1 1 1 1 2 2 20
30 84 7 1 1 1 1 1 4 21
30 84 8 1 1 1 1 1 2 2 21
30 88 6 1 1 1 1 4 22
30 88 7 1 1 1 1 2 2 22
30 90 9 1 1 1 1 1 1 1 5 18
30 92 5 1 1 1 4 23
30 92 6 1 1 1 2 2 23
30 95 8 1 1 1 1 1 1 5 19
30 96 4 1 1 4 24
30 96 5 1 1 2 2 24
31 44 9 1 1 1 1 1 1 1 2 22
31 46 8 1 1 1 1 1 1 2 23
31 48 7 1 1 1 1 1 2 24
31 50 6 1 1 1 1 2 25
31 63 9 1 1 1 1 1 1 1 3 21
31 66 8 1 1 1 1 1 1 3 22
31 69 7 1 1 1 1 1 3 23
31 72 6 1 1 1 1 3 24
31 75 5 1 1 1 3 25
31 80 9 1 1 1 1 1 1 1 4 20
31 84 8 1 1 1 1 1 1 4 21
31 84 9 1 1 1 1 1 1 2 2 21
31 88 7 1 1 1 1 1 4 22
31 88 8 1 1 1 1 1 2 2 22
31 92 6 1 1 1 1 4 23
31 92 7 1 1 1 1 2 2 23
31 95 9 1 1 1 1 1 1 1 5 19
31 96 5 1 1 1 4 24
31 96 6 1 1 1 2 2 24
32 46 9 1 1 1 1 1 1 1 2 23
32 48 8 1 1 1 1 1 1 2 24
32 50 7 1 1 1 1 1 2 25
32 66 9 1 1 1 1 1 1 1 3 22
32 69 8 1 1 1 1 1 1 3 23
32 72 7 1 1 1 1 1 3 24
32 75 6 1 1 1 1 3 25
32 84 9 1 1 1 1 1 1 1 4 21
32 88 8 1 1 1 1 1 1 4 22
32 88 9 1 1 1 1 1 1 2 2 22
32 92 7 1 1 1 1 1 4 23
32 92 8 1 1 1 1 1 2 2 23
32 96 6 1 1 1 1 4 24
32 96 7 1 1 1 1 2 2 24
33 48 9 1 1 1 1 1 1 1 2 24
33 50 8 1 1 1 1 1 1 2 25
33 69 9 1 1 1 1 1 1 1 3 23
33 72 8 1 1 1 1 1 1 3 24
33 75 7 1 1 1 1 1 3 25
33 88 9 1 1 1 1 1 1 1 4 22
33 92 8 1 1 1 1 1 1 4 23
33 92 9 1 1 1 1 1 1 2 2 23
33 96 7 1 1 1 1 1 4 24
33 96 8 1 1 1 1 1 2 2 24
34 50 9 1 1 1 1 1 1 1 2 25
34 72 9 1 1 1 1 1 1 1 3 24
34 75 8 1 1 1 1 1 1 3 25
34 92 9 1 1 1 1 1 1 1 4 23
34 96 8 1 1 1 1 1 1 4 24
34 96 9 1 1 1 1 1 1 2 2 24
35 75 9 1 1 1 1 1 1 1 3 25
35 96 9 1 1 1 1 1 1 1 4 24
The second part looked for identical sets of the first three items (within first 14 bytes when produced--above is edited to give more space), as these would be the ones where A could correctly answer "No" to B's question:
12 48 4 1 3 4 4
12 48 4 2 2 2 6
13 36 3 1 6 6
13 36 3 2 2 9
13 48 5 1 1 3 4 4
13 48 5 1 2 2 2 6
14 36 4 1 1 6 6
14 36 4 1 2 2 9
14 40 3 1 5 8
14 40 3 2 2 10
14 48 6 1 1 1 3 4 4
14 48 6 1 1 2 2 2 6
14 72 3 2 6 6
14 72 3 3 3 8
14 96 5 1 2 3 4 4
14 96 5 2 2 2 2 6
15 36 5 1 1 1 6 6
15 36 5 1 1 2 2 9
15 40 4 1 1 5 8
15 40 4 1 2 2 10
15 48 7 1 1 1 1 3 4 4
15 48 7 1 1 1 2 2 2 6
15 72 4 1 2 6 6
15 72 4 1 3 3 8
15 72 4 1 3 3 8
15 72 4 2 2 2 9
15 96 4 1 4 4 6
15 96 4 2 2 3 8
15 96 6 1 1 2 3 4 4
15 96 6 1 2 2 2 2 6
16 36 6 1 1 1 1 6 6
16 36 6 1 1 1 2 2 9
16 40 5 1 1 1 5 8
16 40 5 1 1 2 2 10
16 48 8 1 1 1 1 1 3 4 4
16 48 8 1 1 1 1 2 2 2 6
16 72 5 1 1 2 6 6
16 72 5 1 1 3 3 8
16 72 5 1 1 3 3 8
16 72 5 1 2 2 2 9
16 80 4 1 2 5 8
16 80 4 2 2 2 10
16 90 3 2 5 9
16 90 3 3 3 10
16 96 5 1 1 4 4 6
16 96 5 1 2 2 3 8
16 96 7 1 1 1 2 3 4 4
16 96 7 1 1 2 2 2 2 6
17 36 7 1 1 1 1 1 6 6
17 36 7 1 1 1 1 2 2 9
17 40 6 1 1 1 1 5 8
17 40 6 1 1 1 2 2 10
17 48 9 1 1 1 1 1 1 3 4 4
17 48 9 1 1 1 1 1 2 2 2 6
17 72 6 1 1 1 2 6 6
17 72 6 1 1 1 3 3 8
17 72 6 1 1 1 3 3 8
17 72 6 1 1 2 2 2 9
17 80 5 1 1 2 5 8
17 80 5 1 2 2 2 10
17 90 4 1 2 5 9
17 90 4 1 3 3 10
17 96 6 1 1 1 4 4 6
17 96 6 1 1 2 2 3 8
17 96 8 1 1 1 1 2 3 4 4
17 96 8 1 1 1 2 2 2 2 6
18 36 8 1 1 1 1 1 1 6 6
18 36 8 1 1 1 1 1 2 2 9
18 40 7 1 1 1 1 1 5 8
18 40 7 1 1 1 1 2 2 10
18 72 7 1 1 1 1 2 6 6
18 72 7 1 1 1 1 3 3 8
18 72 7 1 1 1 1 3 3 8
18 72 7 1 1 1 2 2 2 9
18 80 6 1 1 1 2 5 8
18 80 6 1 1 2 2 2 10
18 90 5 1 1 2 5 9
18 90 5 1 1 3 3 10
18 96 7 1 1 1 1 4 4 6
18 96 7 1 1 1 2 2 3 8
18 96 9 1 1 1 1 1 2 3 4 4
18 96 9 1 1 1 1 2 2 2 2 6
19 36 9 1 1 1 1 1 1 1 6 6
19 36 9 1 1 1 1 1 1 2 2 9
19 40 8 1 1 1 1 1 1 5 8
19 40 8 1 1 1 1 1 2 2 10
19 72 8 1 1 1 1 1 2 6 6
19 72 8 1 1 1 1 1 3 3 8
19 72 8 1 1 1 1 1 3 3 8
19 72 8 1 1 1 1 2 2 2 9
19 80 7 1 1 1 1 2 5 8
19 80 7 1 1 1 2 2 2 10
19 90 6 1 1 1 2 5 9
19 90 6 1 1 1 3 3 10
19 96 8 1 1 1 1 1 4 4 6
19 96 8 1 1 1 1 2 2 3 8
20 40 9 1 1 1 1 1 1 1 5 8
20 40 9 1 1 1 1 1 1 2 2 10
20 72 9 1 1 1 1 1 1 2 6 6
20 72 9 1 1 1 1 1 1 3 3 8
20 72 9 1 1 1 1 1 1 3 3 8
20 72 9 1 1 1 1 1 2 2 2 9
20 80 8 1 1 1 1 1 2 5 8
20 80 8 1 1 1 1 2 2 2 10
20 90 3 1 9 10
20 90 3 2 3 15
20 90 7 1 1 1 1 2 5 9
20 90 7 1 1 1 1 3 3 10
20 96 9 1 1 1 1 1 1 4 4 6
20 96 9 1 1 1 1 1 2 2 3 8
21 80 9 1 1 1 1 1 1 2 5 8
21 80 9 1 1 1 1 1 2 2 2 10
21 90 4 1 1 9 10
21 90 4 1 2 3 15
21 90 8 1 1 1 1 1 2 5 9
21 90 8 1 1 1 1 1 3 3 10
21 96 3 1 8 12
21 96 3 2 3 16
22 90 5 1 1 1 9 10
22 90 5 1 1 2 3 15
22 90 9 1 1 1 1 1 1 2 5 9
22 90 9 1 1 1 1 1 1 3 3 10
22 96 4 1 1 8 12
22 96 4 1 2 3 16
23 90 6 1 1 1 1 9 10
23 90 6 1 1 1 2 3 15
23 96 5 1 1 1 8 12
23 96 5 1 1 2 3 16
24 90 7 1 1 1 1 1 9 10
24 90 7 1 1 1 1 2 3 15
24 96 6 1 1 1 1 8 12
24 96 6 1 1 1 2 3 16
25 90 8 1 1 1 1 1 1 9 10
25 90 8 1 1 1 1 1 2 3 15
25 96 7 1 1 1 1 1 8 12
25 96 7 1 1 1 1 2 3 16
26 90 9 1 1 1 1 1 1 1 9 10
26 90 9 1 1 1 1 1 1 2 3 15
26 96 8 1 1 1 1 1 1 8 12
26 96 8 1 1 1 1 1 2 3 16
27 96 9 1 1 1 1 1 1 1 8 12
27 96 9 1 1 1 1 1 1 2 3 16
But since B said he's now able to know A's age, only the pairs for bus numbers 12 and 27 (which B already knows) allow him to determine A's age. However the case of bus number 27 has a 96-year old with at least 6 1-year old children, and we can rule that out now.
The bus number was 12, as was the sum of A's kids' ages. Their ages' product is 48 and so that's A's age, and he has 4 children. The only thing in doubt is their ages: either 1, 3 and two 4-year olds; or three 2-year olds and a 6 year old.
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Posted by Charlie
on 2015-10-30 15:28:09 |
re(2): computer aided solution -- continued
