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67.php
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<!--
By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23.
3
7 4
2 4 6
8 5 9 3
That is, 3 + 7 + 4 + 9 = 23.
Find the maximum total from top to bottom in triangle.txt (right click and 'Save Link/Target As...'), a 15K text file containing a triangle with one-hundred rows.
59
73 41
52 40 09
26 53 06 34
10 51 87 86 81
61 95 66 57 25 68
90 81 80 38 92 67 73
30 28 51 76 81 18 75 44
84 14 95 87 62 81 17 78 58
21 46 71 58 02 79 62 39 31 09
56 34 35 53 78 31 81 18 90 93 15
78 53 04 21 84 93 32 13 97 11 37 51
45 03 81 79 05 18 78 86 13 30 63 99 95
39 87 96 28 03 38 42 17 82 87 58 07 22 57
06 17 51 17 07 93 09 07 75 97 95 78 87 08 53
67 66 59 60 88 99 94 65 55 77 55 34 27 53 78 28
76 40 41 04 87 16 09 42 75 69 23 97 30 60 10 79 87
12 10 44 26 21 36 32 84 98 60 13 12 36 16 63 31 91 35
70 39 06 05 55 27 38 48 28 22 34 35 62 62 15 14 94 89 86
66 56 68 84 96 21 34 34 34 81 62 40 65 54 62 05 98 03 02 60
38 89 46 37 99 54 34 53 36 14 70 26 02 90 45 13 31 61 83 73 47
36 10 63 96 60 49 41 05 37 42 14 58 84 93 96 17 09 43 05 43 06 59
66 57 87 57 61 28 37 51 84 73 79 15 39 95 88 87 43 39 11 86 77 74 18
54 42 05 79 30 49 99 73 46 37 50 02 45 09 54 52 27 95 27 65 19 45 26 45
71 39 17 78 76 29 52 90 18 99 78 19 35 62 71 19 23 65 93 85 49 33 75 09 02
33 24 47 61 60 55 32 88 57 55 91 54 46 57 07 77 98 52 80 99 24 25 46 78 79 05
92 09 13 55 10 67 26 78 76 82 63 49 51 31 24 68 05 57 07 54 69 21 67 43 17 63 12
24 59 06 08 98 74 66 26 61 60 13 03 09 09 24 30 71 08 88 70 72 70 29 90 11 82 41 34
66 82 67 04 36 60 92 77 91 85 62 49 59 61 30 90 29 94 26 41 89 04 53 22 83 41 09 74 90
48 28 26 37 28 52 77 26 51 32 18 98 79 36 62 13 17 08 19 54 89 29 73 68 42 14 08 16 70 37
37 60 69 70 72 71 09 59 13 60 38 13 57 36 09 30 43 89 30 39 15 02 44 73 05 73 26 63 56 86 12
55 55 85 50 62 99 84 77 28 85 03 21 27 22 19 26 82 69 54 04 13 07 85 14 01 15 70 59 89 95 10 19
04 09 31 92 91 38 92 86 98 75 21 05 64 42 62 84 36 20 73 42 21 23 22 51 51 79 25 45 85 53 03 43 22
75 63 02 49 14 12 89 14 60 78 92 16 44 82 38 30 72 11 46 52 90 27 08 65 78 03 85 41 57 79 39 52 33 48
78 27 56 56 39 13 19 43 86 72 58 95 39 07 04 34 21 98 39 15 39 84 89 69 84 46 37 57 59 35 59 50 26 15 93
42 89 36 27 78 91 24 11 17 41 05 94 07 69 51 96 03 96 47 90 90 45 91 20 50 56 10 32 36 49 04 53 85 92 25 65
52 09 61 30 61 97 66 21 96 92 98 90 06 34 96 60 32 69 68 33 75 84 18 31 71 50 84 63 03 03 19 11 28 42 75 45 45
61 31 61 68 96 34 49 39 05 71 76 59 62 67 06 47 96 99 34 21 32 47 52 07 71 60 42 72 94 56 82 83 84 40 94 87 82 46
01 20 60 14 17 38 26 78 66 81 45 95 18 51 98 81 48 16 53 88 37 52 69 95 72 93 22 34 98 20 54 27 73 61 56 63 60 34 63
93 42 94 83 47 61 27 51 79 79 45 01 44 73 31 70 83 42 88 25 53 51 30 15 65 94 80 44 61 84 12 77 02 62 02 65 94 42 14 94
32 73 09 67 68 29 74 98 10 19 85 48 38 31 85 67 53 93 93 77 47 67 39 72 94 53 18 43 77 40 78 32 29 59 24 06 02 83 50 60 66
32 01 44 30 16 51 15 81 98 15 10 62 86 79 50 62 45 60 70 38 31 85 65 61 64 06 69 84 14 22 56 43 09 48 66 69 83 91 60 40 36 61
92 48 22 99 15 95 64 43 01 16 94 02 99 19 17 69 11 58 97 56 89 31 77 45 67 96 12 73 08 20 36 47 81 44 50 64 68 85 40 81 85 52 09
91 35 92 45 32 84 62 15 19 64 21 66 06 01 52 80 62 59 12 25 88 28 91 50 40 16 22 99 92 79 87 51 21 77 74 77 07 42 38 42 74 83 02 05
46 19 77 66 24 18 05 32 02 84 31 99 92 58 96 72 91 36 62 99 55 29 53 42 12 37 26 58 89 50 66 19 82 75 12 48 24 87 91 85 02 07 03 76 86
99 98 84 93 07 17 33 61 92 20 66 60 24 66 40 30 67 05 37 29 24 96 03 27 70 62 13 04 45 47 59 88 43 20 66 15 46 92 30 04 71 66 78 70 53 99
67 60 38 06 88 04 17 72 10 99 71 07 42 25 54 05 26 64 91 50 45 71 06 30 67 48 69 82 08 56 80 67 18 46 66 63 01 20 08 80 47 07 91 16 03 79 87
18 54 78 49 80 48 77 40 68 23 60 88 58 80 33 57 11 69 55 53 64 02 94 49 60 92 16 35 81 21 82 96 25 24 96 18 02 05 49 03 50 77 06 32 84 27 18 38
68 01 50 04 03 21 42 94 53 24 89 05 92 26 52 36 68 11 85 01 04 42 02 45 15 06 50 04 53 73 25 74 81 88 98 21 67 84 79 97 99 20 95 04 40 46 02 58 87
94 10 02 78 88 52 21 03 88 60 06 53 49 71 20 91 12 65 07 49 21 22 11 41 58 99 36 16 09 48 17 24 52 36 23 15 72 16 84 56 02 99 43 76 81 71 29 39 49 17
64 39 59 84 86 16 17 66 03 09 43 06 64 18 63 29 68 06 23 07 87 14 26 35 17 12 98 41 53 64 78 18 98 27 28 84 80 67 75 62 10 11 76 90 54 10 05 54 41 39 66
43 83 18 37 32 31 52 29 95 47 08 76 35 11 04 53 35 43 34 10 52 57 12 36 20 39 40 55 78 44 07 31 38 26 08 15 56 88 86 01 52 62 10 24 32 05 60 65 53 28 57 99
03 50 03 52 07 73 49 92 66 80 01 46 08 67 25 36 73 93 07 42 25 53 13 96 76 83 87 90 54 89 78 22 78 91 73 51 69 09 79 94 83 53 09 40 69 62 10 79 49 47 03 81 30
71 54 73 33 51 76 59 54 79 37 56 45 84 17 62 21 98 69 41 95 65 24 39 37 62 03 24 48 54 64 46 82 71 78 33 67 09 16 96 68 52 74 79 68 32 21 13 78 96 60 09 69 20 36
73 26 21 44 46 38 17 83 65 98 07 23 52 46 61 97 33 13 60 31 70 15 36 77 31 58 56 93 75 68 21 36 69 53 90 75 25 82 39 50 65 94 29 30 11 33 11 13 96 02 56 47 07 49 02
76 46 73 30 10 20 60 70 14 56 34 26 37 39 48 24 55 76 84 91 39 86 95 61 50 14 53 93 64 67 37 31 10 84 42 70 48 20 10 72 60 61 84 79 69 65 99 73 89 25 85 48 92 56 97 16
03 14 80 27 22 30 44 27 67 75 79 32 51 54 81 29 65 14 19 04 13 82 04 91 43 40 12 52 29 99 07 76 60 25 01 07 61 71 37 92 40 47 99 66 57 01 43 44 22 40 53 53 09 69 26 81 07
49 80 56 90 93 87 47 13 75 28 87 23 72 79 32 18 27 20 28 10 37 59 21 18 70 04 79 96 03 31 45 71 81 06 14 18 17 05 31 50 92 79 23 47 09 39 47 91 43 54 69 47 42 95 62 46 32 85
37 18 62 85 87 28 64 05 77 51 47 26 30 65 05 70 65 75 59 80 42 52 25 20 44 10 92 17 71 95 52 14 77 13 24 55 11 65 26 91 01 30 63 15 49 48 41 17 67 47 03 68 20 90 98 32 04 40 68
90 51 58 60 06 55 23 68 05 19 76 94 82 36 96 43 38 90 87 28 33 83 05 17 70 83 96 93 06 04 78 47 80 06 23 84 75 23 87 72 99 14 50 98 92 38 90 64 61 58 76 94 36 66 87 80 51 35 61 38
57 95 64 06 53 36 82 51 40 33 47 14 07 98 78 65 39 58 53 06 50 53 04 69 40 68 36 69 75 78 75 60 03 32 39 24 74 47 26 90 13 40 44 71 90 76 51 24 36 50 25 45 70 80 61 80 61 43 90 64 11
18 29 86 56 68 42 79 10 42 44 30 12 96 18 23 18 52 59 02 99 67 46 60 86 43 38 55 17 44 93 42 21 55 14 47 34 55 16 49 24 23 29 96 51 55 10 46 53 27 92 27 46 63 57 30 65 43 27 21 20 24 83
81 72 93 19 69 52 48 01 13 83 92 69 20 48 69 59 20 62 05 42 28 89 90 99 32 72 84 17 08 87 36 03 60 31 36 36 81 26 97 36 48 54 56 56 27 16 91 08 23 11 87 99 33 47 02 14 44 73 70 99 43 35 33
90 56 61 86 56 12 70 59 63 32 01 15 81 47 71 76 95 32 65 80 54 70 34 51 40 45 33 04 64 55 78 68 88 47 31 47 68 87 03 84 23 44 89 72 35 08 31 76 63 26 90 85 96 67 65 91 19 14 17 86 04 71 32 95
37 13 04 22 64 37 37 28 56 62 86 33 07 37 10 44 52 82 52 06 19 52 57 75 90 26 91 24 06 21 14 67 76 30 46 14 35 89 89 41 03 64 56 97 87 63 22 34 03 79 17 45 11 53 25 56 96 61 23 18 63 31 37 37 47
77 23 26 70 72 76 77 04 28 64 71 69 14 85 96 54 95 48 06 62 99 83 86 77 97 75 71 66 30 19 57 90 33 01 60 61 14 12 90 99 32 77 56 41 18 14 87 49 10 14 90 64 18 50 21 74 14 16 88 05 45 73 82 47 74 44
22 97 41 13 34 31 54 61 56 94 03 24 59 27 98 77 04 09 37 40 12 26 87 09 71 70 07 18 64 57 80 21 12 71 83 94 60 39 73 79 73 19 97 32 64 29 41 07 48 84 85 67 12 74 95 20 24 52 41 67 56 61 29 93 35 72 69
72 23 63 66 01 11 07 30 52 56 95 16 65 26 83 90 50 74 60 18 16 48 43 77 37 11 99 98 30 94 91 26 62 73 45 12 87 73 47 27 01 88 66 99 21 41 95 80 02 53 23 32 61 48 32 43 43 83 14 66 95 91 19 81 80 67 25 88
08 62 32 18 92 14 83 71 37 96 11 83 39 99 05 16 23 27 10 67 02 25 44 11 55 31 46 64 41 56 44 74 26 81 51 31 45 85 87 09 81 95 22 28 76 69 46 48 64 87 67 76 27 89 31 11 74 16 62 03 60 94 42 47 09 34 94 93 72
56 18 90 18 42 17 42 32 14 86 06 53 33 95 99 35 29 15 44 20 49 59 25 54 34 59 84 21 23 54 35 90 78 16 93 13 37 88 54 19 86 67 68 55 66 84 65 42 98 37 87 56 33 28 58 38 28 38 66 27 52 21 81 15 08 22 97 32 85 27
91 53 40 28 13 34 91 25 01 63 50 37 22 49 71 58 32 28 30 18 68 94 23 83 63 62 94 76 80 41 90 22 82 52 29 12 18 56 10 08 35 14 37 57 23 65 67 40 72 39 93 39 70 89 40 34 07 46 94 22 20 05 53 64 56 30 05 56 61 88 27
23 95 11 12 37 69 68 24 66 10 87 70 43 50 75 07 62 41 83 58 95 93 89 79 45 39 02 22 05 22 95 43 62 11 68 29 17 40 26 44 25 71 87 16 70 85 19 25 59 94 90 41 41 80 61 70 55 60 84 33 95 76 42 63 15 09 03 40 38 12 03 32
09 84 56 80 61 55 85 97 16 94 82 94 98 57 84 30 84 48 93 90 71 05 95 90 73 17 30 98 40 64 65 89 07 79 09 19 56 36 42 30 23 69 73 72 07 05 27 61 24 31 43 48 71 84 21 28 26 65 65 59 65 74 77 20 10 81 61 84 95 08 52 23 70
47 81 28 09 98 51 67 64 35 51 59 36 92 82 77 65 80 24 72 53 22 07 27 10 21 28 30 22 48 82 80 48 56 20 14 43 18 25 50 95 90 31 77 08 09 48 44 80 90 22 93 45 82 17 13 96 25 26 08 73 34 99 06 49 24 06 83 51 40 14 15 10 25 01
54 25 10 81 30 64 24 74 75 80 36 75 82 60 22 69 72 91 45 67 03 62 79 54 89 74 44 83 64 96 66 73 44 30 74 50 37 05 09 97 70 01 60 46 37 91 39 75 75 18 58 52 72 78 51 81 86 52 08 97 01 46 43 66 98 62 81 18 70 93 73 08 32 46 34
96 80 82 07 59 71 92 53 19 20 88 66 03 26 26 10 24 27 50 82 94 73 63 08 51 33 22 45 19 13 58 33 90 15 22 50 36 13 55 06 35 47 82 52 33 61 36 27 28 46 98 14 73 20 73 32 16 26 80 53 47 66 76 38 94 45 02 01 22 52 47 96 64 58 52 39
88 46 23 39 74 63 81 64 20 90 33 33 76 55 58 26 10 46 42 26 74 74 12 83 32 43 09 02 73 55 86 54 85 34 28 23 29 79 91 62 47 41 82 87 99 22 48 90 20 05 96 75 95 04 43 28 81 39 81 01 28 42 78 25 39 77 90 57 58 98 17 36 73 22 63 74 51
29 39 74 94 95 78 64 24 38 86 63 87 93 06 70 92 22 16 80 64 29 52 20 27 23 50 14 13 87 15 72 96 81 22 08 49 72 30 70 24 79 31 16 64 59 21 89 34 96 91 48 76 43 53 88 01 57 80 23 81 90 79 58 01 80 87 17 99 86 90 72 63 32 69 14 28 88 69
37 17 71 95 56 93 71 35 43 45 04 98 92 94 84 96 11 30 31 27 31 60 92 03 48 05 98 91 86 94 35 90 90 08 48 19 33 28 68 37 59 26 65 96 50 68 22 07 09 49 34 31 77 49 43 06 75 17 81 87 61 79 52 26 27 72 29 50 07 98 86 01 17 10 46 64 24 18 56
51 30 25 94 88 85 79 91 40 33 63 84 49 67 98 92 15 26 75 19 82 05 18 78 65 93 61 48 91 43 59 41 70 51 22 15 92 81 67 91 46 98 11 11 65 31 66 10 98 65 83 21 05 56 05 98 73 67 46 74 69 34 08 30 05 52 07 98 32 95 30 94 65 50 24 63 28 81 99 57
19 23 61 36 09 89 71 98 65 17 30 29 89 26 79 74 94 11 44 48 97 54 81 55 39 66 69 45 28 47 13 86 15 76 74 70 84 32 36 33 79 20 78 14 41 47 89 28 81 05 99 66 81 86 38 26 06 25 13 60 54 55 23 53 27 05 89 25 23 11 13 54 59 54 56 34 16 24 53 44 06
13 40 57 72 21 15 60 08 04 19 11 98 34 45 09 97 86 71 03 15 56 19 15 44 97 31 90 04 87 87 76 08 12 30 24 62 84 28 12 85 82 53 99 52 13 94 06 65 97 86 09 50 94 68 69 74 30 67 87 94 63 07 78 27 80 36 69 41 06 92 32 78 37 82 30 05 18 87 99 72 19 99
44 20 55 77 69 91 27 31 28 81 80 27 02 07 97 23 95 98 12 25 75 29 47 71 07 47 78 39 41 59 27 76 13 15 66 61 68 35 69 86 16 53 67 63 99 85 41 56 08 28 33 40 94 76 90 85 31 70 24 65 84 65 99 82 19 25 54 37 21 46 33 02 52 99 51 33 26 04 87 02 08 18 96
54 42 61 45 91 06 64 79 80 82 32 16 83 63 42 49 19 78 65 97 40 42 14 61 49 34 04 18 25 98 59 30 82 72 26 88 54 36 21 75 03 88 99 53 46 51 55 78 22 94 34 40 68 87 84 25 30 76 25 08 92 84 42 61 40 38 09 99 40 23 29 39 46 55 10 90 35 84 56 70 63 23 91 39
52 92 03 71 89 07 09 37 68 66 58 20 44 92 51 56 13 71 79 99 26 37 02 06 16 67 36 52 58 16 79 73 56 60 59 27 44 77 94 82 20 50 98 33 09 87 94 37 40 83 64 83 58 85 17 76 53 02 83 52 22 27 39 20 48 92 45 21 09 42 24 23 12 37 52 28 50 78 79 20 86 62 73 20 59
54 96 80 15 91 90 99 70 10 09 58 90 93 50 81 99 54 38 36 10 30 11 35 84 16 45 82 18 11 97 36 43 96 79 97 65 40 48 23 19 17 31 64 52 65 65 37 32 65 76 99 79 34 65 79 27 55 33 03 01 33 27 61 28 66 08 04 70 49 46 48 83 01 45 19 96 13 81 14 21 31 79 93 85 50 05
92 92 48 84 59 98 31 53 23 27 15 22 79 95 24 76 05 79 16 93 97 89 38 89 42 83 02 88 94 95 82 21 01 97 48 39 31 78 09 65 50 56 97 61 01 07 65 27 21 23 14 15 80 97 44 78 49 35 33 45 81 74 34 05 31 57 09 38 94 07 69 54 69 32 65 68 46 68 78 90 24 28 49 51 45 86 35
41 63 89 76 87 31 86 09 46 14 87 82 22 29 47 16 13 10 70 72 82 95 48 64 58 43 13 75 42 69 21 12 67 13 64 85 58 23 98 09 37 76 05 22 31 12 66 50 29 99 86 72 45 25 10 28 19 06 90 43 29 31 67 79 46 25 74 14 97 35 76 37 65 46 23 82 06 22 30 76 93 66 94 17 96 13 20 72
63 40 78 08 52 09 90 41 70 28 36 14 46 44 85 96 24 52 58 15 87 37 05 98 99 39 13 61 76 38 44 99 83 74 90 22 53 80 56 98 30 51 63 39 44 30 91 91 04 22 27 73 17 35 53 18 35 45 54 56 27 78 48 13 69 36 44 38 71 25 30 56 15 22 73 43 32 69 59 25 93 83 45 11 34 94 44 39 92
12 36 56 88 13 96 16 12 55 54 11 47 19 78 17 17 68 81 77 51 42 55 99 85 66 27 81 79 93 42 65 61 69 74 14 01 18 56 12 01 58 37 91 22 42 66 83 25 19 04 96 41 25 45 18 69 96 88 36 93 10 12 98 32 44 83 83 04 72 91 04 27 73 07 34 37 71 60 59 31 01 54 54 44 96 93 83 36 04 45
30 18 22 20 42 96 65 79 17 41 55 69 94 81 29 80 91 31 85 25 47 26 43 49 02 99 34 67 99 76 16 14 15 93 08 32 99 44 61 77 67 50 43 55 87 55 53 72 17 46 62 25 50 99 73 05 93 48 17 31 70 80 59 09 44 59 45 13 74 66 58 94 87 73 16 14 85 38 74 99 64 23 79 28 71 42 20 37 82 31 23
51 96 39 65 46 71 56 13 29 68 53 86 45 33 51 49 12 91 21 21 76 85 02 17 98 15 46 12 60 21 88 30 92 83 44 59 42 50 27 88 46 86 94 73 45 54 23 24 14 10 94 21 20 34 23 51 04 83 99 75 90 63 60 16 22 33 83 70 11 32 10 50 29 30 83 46 11 05 31 17 86 42 49 01 44 63 28 60 07 78 95 40
44 61 89 59 04 49 51 27 69 71 46 76 44 04 09 34 56 39 15 06 94 91 75 90 65 27 56 23 74 06 23 33 36 69 14 39 05 34 35 57 33 22 76 46 56 10 61 65 98 09 16 69 04 62 65 18 99 76 49 18 72 66 73 83 82 40 76 31 89 91 27 88 17 35 41 35 32 51 32 67 52 68 74 85 80 57 07 11 62 66 47 22 67
65 37 19 97 26 17 16 24 24 17 50 37 64 82 24 36 32 11 68 34 69 31 32 89 79 93 96 68 49 90 14 23 04 04 67 99 81 74 70 74 36 96 68 09 64 39 88 35 54 89 96 58 66 27 88 97 32 14 06 35 78 20 71 06 85 66 57 02 58 91 72 05 29 56 73 48 86 52 09 93 22 57 79 42 12 01 31 68 17 59 63 76 07 77
73 81 14 13 17 20 11 09 01 83 08 85 91 70 84 63 62 77 37 07 47 01 59 95 39 69 39 21 99 09 87 02 97 16 92 36 74 71 90 66 33 73 73 75 52 91 11 12 26 53 05 26 26 48 61 50 90 65 01 87 42 47 74 35 22 73 24 26 56 70 52 05 48 41 31 18 83 27 21 39 80 85 26 08 44 02 71 07 63 22 05 52 19 08 20
17 25 21 11 72 93 33 49 64 23 53 82 03 13 91 65 85 02 40 05 42 31 77 42 05 36 06 54 04 58 07 76 87 83 25 57 66 12 74 33 85 37 74 32 20 69 03 97 91 68 82 44 19 14 89 28 85 85 80 53 34 87 58 98 88 78 48 65 98 40 11 57 10 67 70 81 60 79 74 72 97 59 79 47 30 20 54 80 89 91 14 05 33 36 79 39
60 85 59 39 60 07 57 76 77 92 06 35 15 72 23 41 45 52 95 18 64 79 86 53 56 31 69 11 91 31 84 50 44 82 22 81 41 40 30 42 30 91 48 94 74 76 64 58 74 25 96 57 14 19 03 99 28 83 15 75 99 01 89 85 79 50 03 95 32 67 44 08 07 41 62 64 29 20 14 76 26 55 48 71 69 66 19 72 44 25 14 01 48 74 12 98 07
64 66 84 24 18 16 27 48 20 14 47 69 30 86 48 40 23 16 61 21 51 50 26 47 35 33 91 28 78 64 43 68 04 79 51 08 19 60 52 95 06 68 46 86 35 97 27 58 04 65 30 58 99 12 12 75 91 39 50 31 42 64 70 04 46 07 98 73 98 93 37 89 77 91 64 71 64 65 66 21 78 62 81 74 42 20 83 70 73 95 78 45 92 27 34 53 71 15
30 11 85 31 34 71 13 48 05 14 44 03 19 67 23 73 19 57 06 90 94 72 57 69 81 62 59 68 88 57 55 69 49 13 07 87 97 80 89 05 71 05 05 26 38 40 16 62 45 99 18 38 98 24 21 26 62 74 69 04 85 57 77 35 58 67 91 79 79 57 86 28 66 34 72 51 76 78 36 95 63 90 08 78 47 63 45 31 22 70 52 48 79 94 15 77 61 67 68
23 33 44 81 80 92 93 75 94 88 23 61 39 76 22 03 28 94 32 06 49 65 41 34 18 23 08 47 62 60 03 63 33 13 80 52 31 54 73 43 70 26 16 69 57 87 83 31 03 93 70 81 47 95 77 44 29 68 39 51 56 59 63 07 25 70 07 77 43 53 64 03 94 42 95 39 18 01 66 21 16 97 20 50 90 16 70 10 95 69 29 06 25 61 41 26 15 59 63 35
NOTE: This is a much more difficult version of Problem 18. It is not possible to try every route to solve this problem, as there are 299 altogether! If you could check one trillion (1012) routes every second it would take over twenty billion years to check them all. There is an efficient algorithm to solve it. ;o)
-->
<?php $startTime = microtime(true);
//needed to take out any leading 0 for number under 10 for this to work
$tri[0] = array(59);
$tri[1] = array(73,41);
$tri[2] = array(52,40,9);
$tri[3] = array(26,53,6,34);
$tri[4] = array(10,51,87,86,81);
$tri[5] = array(61,95,66,57,25,68);
$tri[6] = array(90,81,80,38,92,67,73);
$tri[7] = array(30,28,51,76,81,18,75,44);
$tri[8] = array(84,14,95,87,62,81,17,78,58);
$tri[9] = array(21,46,71,58,2,79,62,39,31,9);
$tri[10] = array(56,34,35,53,78,31,81,18,90,93,15);
$tri[11] = array(78,53,4,21,84,93,32,13,97,11,37,51);
$tri[12] = array(45,3,81,79,5,18,78,86,13,30,63,99,95);
$tri[13] = array(39,87,96,28,3,38,42,17,82,87,58,7,22,57);
$tri[14] = array(06,17,51,17,7,93,9,7,75,97,95,78,87,8,53);
$tri[15] = array(67,66,59,60,88,99,94,65,55,77,55,34,27,53,78,28);
$tri[16] = array(76,40,41,4,87,16,9,42,75,69,23,97,30,60,10,79,87);
$tri[17] = array(12,10,44,26,21,36,32,84,98,60,13,12,36,16,63,31,91,35);
$tri[18] = array(70,39,6,5,55,27,38,48,28,22,34,35,62,62,15,14,94,89,86);
$tri[19] = array(66,56,68,84,96,21,34,34,34,81,62,40,65,54,62,5,98,3,2,60);
$tri[20] = array(38,89,46,37,99,54,34,53,36,14,70,26,2,90,45,13,31,61,83,73,47);
$tri[21] = array(36,10,63,96,60,49,41,5,37,42,14,58,84,93,96,17,9,43,5,43,6,59);
$tri[22] = array(66,57,87,57,61,28,37,51,84,73,79,15,39,95,88,87,43,39,11,86,77,74,18);
$tri[23] = array(54,42,5,79,30,49,99,73,46,37,50,2,45,9,54,52,27,95,27,65,19,45,26,45);
$tri[24] = array(71,39,17,78,76,29,52,90,18,99,78,19,35,62,71,19,23,65,93,85,49,33,75,9,2);
$tri[25] = array(33,24,47,61,60,55,32,88,57,55,91,54,46,57,7,77,98,52,80,99,24,25,46,78,79,5);
$tri[26] = array(92,9,13,55,10,67,26,78,76,82,63,49,51,31,24,68,5,57,7,54,69,21,67,43,17,63,12);
$tri[27] = array(24,59,6,8,98,74,66,26,61,60,13,3,9,9,24,30,71,8,88,70,72,70,29,90,11,82,41,34);
$tri[28] = array(66,82,67,4,36,60,92,77,91,85,62,49,59,61,30,90,29,94,26,41,89,4,53,22,83,41,9,74,90);
$tri[29] = array(48,28,26,37,28,52,77,26,51,32,18,98,79,36,62,13,17,8,19,54,89,29,73,68,42,14,8,16,70,37);
$tri[30] = array(37,60,69,70,72,71,9,59,13,60,38,13,57,36,9,30,43,89,30,39,15,2,44,73,5,73,26,63,56,86,12);
$tri[31] = array(55,55,85,50,62,99,84,77,28,85,3,21,27,22,19,26,82,69,54,4,13,7,85,14,1,15,70,59,89,95,10,19);
$tri[32] = array(04,9,31,92,91,38,92,86,98,75,21,5,64,42,62,84,36,20,73,42,21,23,22,51,51,79,25,45,85,53,3,43,22);
$tri[33] = array(75,63,2,49,14,12,89,14,60,78,92,16,44,82,38,30,72,11,46,52,90,27,8,65,78,3,85,41,57,79,39,52,33,48);
$tri[34] = array(78,27,56,56,39,13,19,43,86,72,58,95,39,7,4,34,21,98,39,15,39,84,89,69,84,46,37,57,59,35,59,50,26,15,93);
$tri[35] = array(42,89,36,27,78,91,24,11,17,41,5,94,7,69,51,96,3,96,47,90,90,45,91,20,50,56,10,32,36,49,4,53,85,92,25,65);
$tri[36] = array(52,9,61,30,61,97,66,21,96,92,98,90,6,34,96,60,32,69,68,33,75,84,18,31,71,50,84,63,3,3,19,11,28,42,75,45,45);
$tri[37] = array(61,31,61,68,96,34,49,39,5,71,76,59,62,67,6,47,96,99,34,21,32,47,52,7,71,60,42,72,94,56,82,83,84,40,94,87,82,46);
$tri[38] = array(01,20,60,14,17,38,26,78,66,81,45,95,18,51,98,81,48,16,53,88,37,52,69,95,72,93,22,34,98,20,54,27,73,61,56,63,60,34,63);
$tri[39] = array(93,42,94,83,47,61,27,51,79,79,45,1,44,73,31,70,83,42,88,25,53,51,30,15,65,94,80,44,61,84,12,77,2,62,2,65,94,42,14,94);
$tri[40] = array(32,73,9,67,68,29,74,98,10,19,85,48,38,31,85,67,53,93,93,77,47,67,39,72,94,53,18,43,77,40,78,32,29,59,24,6,2,83,50,60,66);
$tri[41] = array(32,1,44,30,16,51,15,81,98,15,10,62,86,79,50,62,45,60,70,38,31,85,65,61,64,6,69,84,14,22,56,43,9,48,66,69,83,91,60,40,36,61);
$tri[42] = array(92,48,22,99,15,95,64,43,1,16,94,2,99,19,17,69,11,58,97,56,89,31,77,45,67,96,12,73,8,20,36,47,81,44,50,64,68,85,40,81,85,52,9);
$tri[43] = array(91,35,92,45,32,84,62,15,19,64,21,66,6,1,52,80,62,59,12,25,88,28,91,50,40,16,22,99,92,79,87,51,21,77,74,77,7,42,38,42,74,83,2,5);
$tri[44] = array(46,19,77,66,24,18,5,32,2,84,31,99,92,58,96,72,91,36,62,99,55,29,53,42,12,37,26,58,89,50,66,19,82,75,12,48,24,87,91,85,2,7,3,76,86);
$tri[45] = array(99,98,84,93,7,17,33,61,92,20,66,60,24,66,40,30,67,5,37,29,24,96,3,27,70,62,13,4,45,47,59,88,43,20,66,15,46,92,30,4,71,66,78,70,53,99);
$tri[46] = array(67,60,38,6,88,4,17,72,10,99,71,7,42,25,54,5,26,64,91,50,45,71,6,30,67,48,69,82,8,56,80,67,18,46,66,63,1,20,8,80,47,7,91,16,3,79,87);
$tri[47] = array(18,54,78,49,80,48,77,40,68,23,60,88,58,80,33,57,11,69,55,53,64,2,94,49,60,92,16,35,81,21,82,96,25,24,96,18,2,5,49,3,50,77,6,32,84,27,18,38);
$tri[48] = array(68,1,50,4,3,21,42,94,53,24,89,5,92,26,52,36,68,11,85,1,4,42,2,45,15,6,50,4,53,73,25,74,81,88,98,21,67,84,79,97,99,20,95,4,40,46,2,58,87);
$tri[49] = array(94,10,2,78,88,52,21,3,88,60,6,53,49,71,20,91,12,65,7,49,21,22,11,41,58,99,36,16,9,48,17,24,52,36,23,15,72,16,84,56,2,99,43,76,81,71,29,39,49,17);
$tri[50] = array(64,39,59,84,86,16,17,66,3,9,43,6,64,18,63,29,68,6,23,7,87,14,26,35,17,12,98,41,53,64,78,18,98,27,28,84,80,67,75,62,10,11,76,90,54,10,5,54,41,39,66);
$tri[51] = array(43,83,18,37,32,31,52,29,95,47,8,76,35,11,4,53,35,43,34,10,52,57,12,36,20,39,40,55,78,44,7,31,38,26,8,15,56,88,86,1,52,62,10,24,32,5,60,65,53,28,57,99);
$tri[52] = array(03,50,3,52,7,73,49,92,66,80,1,46,8,67,25,36,73,93,7,42,25,53,13,96,76,83,87,90,54,89,78,22,78,91,73,51,69,9,79,94,83,53,9,40,69,62,10,79,49,47,3,81,30);
$tri[53] = array(71,54,73,33,51,76,59,54,79,37,56,45,84,17,62,21,98,69,41,95,65,24,39,37,62,3,24,48,54,64,46,82,71,78,33,67,9,16,96,68,52,74,79,68,32,21,13,78,96,60,9,69,20,36);
$tri[54] = array(73,26,21,44,46,38,17,83,65,98,7,23,52,46,61,97,33,13,60,31,70,15,36,77,31,58,56,93,75,68,21,36,69,53,90,75,25,82,39,50,65,94,29,30,11,33,11,13,96,2,56,47,7,49,2);
$tri[55] = array(76,46,73,30,10,20,60,70,14,56,34,26,37,39,48,24,55,76,84,91,39,86,95,61,50,14,53,93,64,67,37,31,10,84,42,70,48,20,10,72,60,61,84,79,69,65,99,73,89,25,85,48,92,56,97,16);
$tri[56] = array(03,14,80,27,22,30,44,27,67,75,79,32,51,54,81,29,65,14,19,4,13,82,4,91,43,40,12,52,29,99,7,76,60,25,1,7,61,71,37,92,40,47,99,66,57,1,43,44,22,40,53,53,9,69,26,81,7);
$tri[57] = array(49,80,56,90,93,87,47,13,75,28,87,23,72,79,32,18,27,20,28,10,37,59,21,18,70,4,79,96,3,31,45,71,81,6,14,18,17,5,31,50,92,79,23,47,9,39,47,91,43,54,69,47,42,95,62,46,32,85);
$tri[58] = array(37,18,62,85,87,28,64,5,77,51,47,26,30,65,5,70,65,75,59,80,42,52,25,20,44,10,92,17,71,95,52,14,77,13,24,55,11,65,26,91,1,30,63,15,49,48,41,17,67,47,3,68,20,90,98,32,4,40,68);
$tri[59] = array(90,51,58,60,6,55,23,68,5,19,76,94,82,36,96,43,38,90,87,28,33,83,5,17,70,83,96,93,6,4,78,47,80,6,23,84,75,23,87,72,99,14,50,98,92,38,90,64,61,58,76,94,36,66,87,80,51,35,61,38);
$tri[60] = array(57,95,64,6,53,36,82,51,40,33,47,14,7,98,78,65,39,58,53,6,50,53,4,69,40,68,36,69,75,78,75,60,3,32,39,24,74,47,26,90,13,40,44,71,90,76,51,24,36,50,25,45,70,80,61,80,61,43,90,64,11);
$tri[61] = array(18,29,86,56,68,42,79,10,42,44,30,12,96,18,23,18,52,59,2,99,67,46,60,86,43,38,55,17,44,93,42,21,55,14,47,34,55,16,49,24,23,29,96,51,55,10,46,53,27,92,27,46,63,57,30,65,43,27,21,20,24,83);
$tri[62] = array(81,72,93,19,69,52,48,1,13,83,92,69,20,48,69,59,20,62,5,42,28,89,90,99,32,72,84,17,8,87,36,3,60,31,36,36,81,26,97,36,48,54,56,56,27,16,91,8,23,11,87,99,33,47,2,14,44,73,70,99,43,35,33);
$tri[63] = array(90,56,61,86,56,12,70,59,63,32,1,15,81,47,71,76,95,32,65,80,54,70,34,51,40,45,33,4,64,55,78,68,88,47,31,47,68,87,3,84,23,44,89,72,35,8,31,76,63,26,90,85,96,67,65,91,19,14,17,86,4,71,32,95);
$tri[64] = array(37,13,4,22,64,37,37,28,56,62,86,33,7,37,10,44,52,82,52,6,19,52,57,75,90,26,91,24,6,21,14,67,76,30,46,14,35,89,89,41,3,64,56,97,87,63,22,34,3,79,17,45,11,53,25,56,96,61,23,18,63,31,37,37,47);
$tri[65] = array(77,23,26,70,72,76,77,4,28,64,71,69,14,85,96,54,95,48,6,62,99,83,86,77,97,75,71,66,30,19,57,90,33,1,60,61,14,12,90,99,32,77,56,41,18,14,87,49,10,14,90,64,18,50,21,74,14,16,88,5,45,73,82,47,74,44);
$tri[66] = array(22,97,41,13,34,31,54,61,56,94,3,24,59,27,98,77,4,9,37,40,12,26,87,9,71,70,7,18,64,57,80,21,12,71,83,94,60,39,73,79,73,19,97,32,64,29,41,7,48,84,85,67,12,74,95,20,24,52,41,67,56,61,29,93,35,72,69);
$tri[67] = array(72,23,63,66,1,11,7,30,52,56,95,16,65,26,83,90,50,74,60,18,16,48,43,77,37,11,99,98,30,94,91,26,62,73,45,12,87,73,47,27,1,88,66,99,21,41,95,80,2,53,23,32,61,48,32,43,43,83,14,66,95,91,19,81,80,67,25,88);
$tri[68] = array(08,62,32,18,92,14,83,71,37,96,11,83,39,99,5,16,23,27,10,67,2,25,44,11,55,31,46,64,41,56,44,74,26,81,51,31,45,85,87,9,81,95,22,28,76,69,46,48,64,87,67,76,27,89,31,11,74,16,62,3,60,94,42,47,9,34,94,93,72);
$tri[69] = array(56,18,90,18,42,17,42,32,14,86,6,53,33,95,99,35,29,15,44,20,49,59,25,54,34,59,84,21,23,54,35,90,78,16,93,13,37,88,54,19,86,67,68,55,66,84,65,42,98,37,87,56,33,28,58,38,28,38,66,27,52,21,81,15,8,22,97,32,85,27);
$tri[70] = array(91,53,40,28,13,34,91,25,1,63,50,37,22,49,71,58,32,28,30,18,68,94,23,83,63,62,94,76,80,41,90,22,82,52,29,12,18,56,10,8,35,14,37,57,23,65,67,40,72,39,93,39,70,89,40,34,7,46,94,22,20,5,53,64,56,30,5,56,61,88,27);
$tri[71] = array(23,95,11,12,37,69,68,24,66,10,87,70,43,50,75,7,62,41,83,58,95,93,89,79,45,39,2,22,5,22,95,43,62,11,68,29,17,40,26,44,25,71,87,16,70,85,19,25,59,94,90,41,41,80,61,70,55,60,84,33,95,76,42,63,15,9,3,40,38,12,3,32);
$tri[72] = array(09,84,56,80,61,55,85,97,16,94,82,94,98,57,84,30,84,48,93,90,71,5,95,90,73,17,30,98,40,64,65,89,7,79,9,19,56,36,42,30,23,69,73,72,7,5,27,61,24,31,43,48,71,84,21,28,26,65,65,59,65,74,77,20,10,81,61,84,95,8,52,23,70);
$tri[73] = array(47,81,28,9,98,51,67,64,35,51,59,36,92,82,77,65,80,24,72,53,22,7,27,10,21,28,30,22,48,82,80,48,56,20,14,43,18,25,50,95,90,31,77,8,9,48,44,80,90,22,93,45,82,17,13,96,25,26,8,73,34,99,6,49,24,6,83,51,40,14,15,10,25,1);
$tri[74] = array(54,25,10,81,30,64,24,74,75,80,36,75,82,60,22,69,72,91,45,67,3,62,79,54,89,74,44,83,64,96,66,73,44,30,74,50,37,5,9,97,70,1,60,46,37,91,39,75,75,18,58,52,72,78,51,81,86,52,8,97,1,46,43,66,98,62,81,18,70,93,73,8,32,46,34);
$tri[75] = array(96,80,82,7,59,71,92,53,19,20,88,66,3,26,26,10,24,27,50,82,94,73,63,8,51,33,22,45,19,13,58,33,90,15,22,50,36,13,55,6,35,47,82,52,33,61,36,27,28,46,98,14,73,20,73,32,16,26,80,53,47,66,76,38,94,45,2,1,22,52,47,96,64,58,52,39);
$tri[76] = array(88,46,23,39,74,63,81,64,20,90,33,33,76,55,58,26,10,46,42,26,74,74,12,83,32,43,9,2,73,55,86,54,85,34,28,23,29,79,91,62,47,41,82,87,99,22,48,90,20,5,96,75,95,4,43,28,81,39,81,1,28,42,78,25,39,77,90,57,58,98,17,36,73,22,63,74,51);
$tri[77] = array(29,39,74,94,95,78,64,24,38,86,63,87,93,6,70,92,22,16,80,64,29,52,20,27,23,50,14,13,87,15,72,96,81,22,8,49,72,30,70,24,79,31,16,64,59,21,89,34,96,91,48,76,43,53,88,1,57,80,23,81,90,79,58,1,80,87,17,99,86,90,72,63,32,69,14,28,88,69);
$tri[78] = array(37,17,71,95,56,93,71,35,43,45,4,98,92,94,84,96,11,30,31,27,31,60,92,3,48,5,98,91,86,94,35,90,90,8,48,19,33,28,68,37,59,26,65,96,50,68,22,7,9,49,34,31,77,49,43,6,75,17,81,87,61,79,52,26,27,72,29,50,7,98,86,1,17,10,46,64,24,18,56);
$tri[79] = array(51,30,25,94,88,85,79,91,40,33,63,84,49,67,98,92,15,26,75,19,82,5,18,78,65,93,61,48,91,43,59,41,70,51,22,15,92,81,67,91,46,98,11,11,65,31,66,10,98,65,83,21,5,56,5,98,73,67,46,74,69,34,8,30,5,52,7,98,32,95,30,94,65,50,24,63,28,81,99,57);
$tri[80] = array(19,23,61,36,9,89,71,98,65,17,30,29,89,26,79,74,94,11,44,48,97,54,81,55,39,66,69,45,28,47,13,86,15,76,74,70,84,32,36,33,79,20,78,14,41,47,89,28,81,5,99,66,81,86,38,26,6,25,13,60,54,55,23,53,27,5,89,25,23,11,13,54,59,54,56,34,16,24,53,44,6);
$tri[81] = array(13,40,57,72,21,15,60,8,4,19,11,98,34,45,9,97,86,71,3,15,56,19,15,44,97,31,90,4,87,87,76,8,12,30,24,62,84,28,12,85,82,53,99,52,13,94,6,65,97,86,9,50,94,68,69,74,30,67,87,94,63,7,78,27,80,36,69,41,6,92,32,78,37,82,30,5,18,87,99,72,19,99);
$tri[82] = array(44,20,55,77,69,91,27,31,28,81,80,27,2,7,97,23,95,98,12,25,75,29,47,71,7,47,78,39,41,59,27,76,13,15,66,61,68,35,69,86,16,53,67,63,99,85,41,56,8,28,33,40,94,76,90,85,31,70,24,65,84,65,99,82,19,25,54,37,21,46,33,2,52,99,51,33,26,4,87,2,8,18,96);
$tri[83] = array(54,42,61,45,91,6,64,79,80,82,32,16,83,63,42,49,19,78,65,97,40,42,14,61,49,34,4,18,25,98,59,30,82,72,26,88,54,36,21,75,3,88,99,53,46,51,55,78,22,94,34,40,68,87,84,25,30,76,25,8,92,84,42,61,40,38,9,99,40,23,29,39,46,55,10,90,35,84,56,70,63,23,91,39);
$tri[84] = array(52,92,3,71,89,7,9,37,68,66,58,20,44,92,51,56,13,71,79,99,26,37,2,6,16,67,36,52,58,16,79,73,56,60,59,27,44,77,94,82,20,50,98,33,9,87,94,37,40,83,64,83,58,85,17,76,53,2,83,52,22,27,39,20,48,92,45,21,9,42,24,23,12,37,52,28,50,78,79,20,86,62,73,20,59);
$tri[85] = array(54,96,80,15,91,90,99,70,10,9,58,90,93,50,81,99,54,38,36,10,30,11,35,84,16,45,82,18,11,97,36,43,96,79,97,65,40,48,23,19,17,31,64,52,65,65,37,32,65,76,99,79,34,65,79,27,55,33,3,1,33,27,61,28,66,8,4,70,49,46,48,83,1,45,19,96,13,81,14,21,31,79,93,85,50,5);
$tri[86] = array(92,92,48,84,59,98,31,53,23,27,15,22,79,95,24,76,5,79,16,93,97,89,38,89,42,83,2,88,94,95,82,21,1,97,48,39,31,78,9,65,50,56,97,61,1,7,65,27,21,23,14,15,80,97,44,78,49,35,33,45,81,74,34,5,31,57,9,38,94,7,69,54,69,32,65,68,46,68,78,90,24,28,49,51,45,86,35);
$tri[87] = array(41,63,89,76,87,31,86,9,46,14,87,82,22,29,47,16,13,10,70,72,82,95,48,64,58,43,13,75,42,69,21,12,67,13,64,85,58,23,98,9,37,76,5,22,31,12,66,50,29,99,86,72,45,25,10,28,19,6,90,43,29,31,67,79,46,25,74,14,97,35,76,37,65,46,23,82,6,22,30,76,93,66,94,17,96,13,20,72);
$tri[88] = array(63,40,78,8,52,9,90,41,70,28,36,14,46,44,85,96,24,52,58,15,87,37,5,98,99,39,13,61,76,38,44,99,83,74,90,22,53,80,56,98,30,51,63,39,44,30,91,91,4,22,27,73,17,35,53,18,35,45,54,56,27,78,48,13,69,36,44,38,71,25,30,56,15,22,73,43,32,69,59,25,93,83,45,11,34,94,44,39,92);
$tri[89] = array(12,36,56,88,13,96,16,12,55,54,11,47,19,78,17,17,68,81,77,51,42,55,99,85,66,27,81,79,93,42,65,61,69,74,14,1,18,56,12,1,58,37,91,22,42,66,83,25,19,4,96,41,25,45,18,69,96,88,36,93,10,12,98,32,44,83,83,4,72,91,4,27,73,7,34,37,71,60,59,31,1,54,54,44,96,93,83,36,4,45);
$tri[90] = array(30,18,22,20,42,96,65,79,17,41,55,69,94,81,29,80,91,31,85,25,47,26,43,49,2,99,34,67,99,76,16,14,15,93,8,32,99,44,61,77,67,50,43,55,87,55,53,72,17,46,62,25,50,99,73,5,93,48,17,31,70,80,59,9,44,59,45,13,74,66,58,94,87,73,16,14,85,38,74,99,64,23,79,28,71,42,20,37,82,31,23);
$tri[91] = array(51,96,39,65,46,71,56,13,29,68,53,86,45,33,51,49,12,91,21,21,76,85,2,17,98,15,46,12,60,21,88,30,92,83,44,59,42,50,27,88,46,86,94,73,45,54,23,24,14,10,94,21,20,34,23,51,4,83,99,75,90,63,60,16,22,33,83,70,11,32,10,50,29,30,83,46,11,5,31,17,86,42,49,1,44,63,28,60,7,78,95,40);
$tri[92] = array(44,61,89,59,4,49,51,27,69,71,46,76,44,4,9,34,56,39,15,6,94,91,75,90,65,27,56,23,74,6,23,33,36,69,14,39,5,34,35,57,33,22,76,46,56,10,61,65,98,9,16,69,4,62,65,18,99,76,49,18,72,66,73,83,82,40,76,31,89,91,27,88,17,35,41,35,32,51,32,67,52,68,74,85,80,57,7,11,62,66,47,22,67);
$tri[93] = array(65,37,19,97,26,17,16,24,24,17,50,37,64,82,24,36,32,11,68,34,69,31,32,89,79,93,96,68,49,90,14,23,4,4,67,99,81,74,70,74,36,96,68,9,64,39,88,35,54,89,96,58,66,27,88,97,32,14,6,35,78,20,71,6,85,66,57,2,58,91,72,5,29,56,73,48,86,52,9,93,22,57,79,42,12,1,31,68,17,59,63,76,7,77);
$tri[94] = array(73,81,14,13,17,20,11,9,1,83,8,85,91,70,84,63,62,77,37,7,47,1,59,95,39,69,39,21,99,9,87,2,97,16,92,36,74,71,90,66,33,73,73,75,52,91,11,12,26,53,5,26,26,48,61,50,90,65,1,87,42,47,74,35,22,73,24,26,56,70,52,5,48,41,31,18,83,27,21,39,80,85,26,8,44,2,71,7,63,22,5,52,19,8,20);
$tri[95] = array(17,25,21,11,72,93,33,49,64,23,53,82,3,13,91,65,85,2,40,5,42,31,77,42,5,36,6,54,4,58,7,76,87,83,25,57,66,12,74,33,85,37,74,32,20,69,3,97,91,68,82,44,19,14,89,28,85,85,80,53,34,87,58,98,88,78,48,65,98,40,11,57,10,67,70,81,60,79,74,72,97,59,79,47,30,20,54,80,89,91,14,5,33,36,79,39);
$tri[96] = array(60,85,59,39,60,7,57,76,77,92,6,35,15,72,23,41,45,52,95,18,64,79,86,53,56,31,69,11,91,31,84,50,44,82,22,81,41,40,30,42,30,91,48,94,74,76,64,58,74,25,96,57,14,19,3,99,28,83,15,75,99,1,89,85,79,50,3,95,32,67,44,8,7,41,62,64,29,20,14,76,26,55,48,71,69,66,19,72,44,25,14,1,48,74,12,98,7);
$tri[97] = array(64,66,84,24,18,16,27,48,20,14,47,69,30,86,48,40,23,16,61,21,51,50,26,47,35,33,91,28,78,64,43,68,4,79,51,8,19,60,52,95,6,68,46,86,35,97,27,58,4,65,30,58,99,12,12,75,91,39,50,31,42,64,70,4,46,7,98,73,98,93,37,89,77,91,64,71,64,65,66,21,78,62,81,74,42,20,83,70,73,95,78,45,92,27,34,53,71,15);
$tri[98] = array(30,11,85,31,34,71,13,48,5,14,44,3,19,67,23,73,19,57,6,90,94,72,57,69,81,62,59,68,88,57,55,69,49,13,7,87,97,80,89,5,71,5,5,26,38,40,16,62,45,99,18,38,98,24,21,26,62,74,69,4,85,57,77,35,58,67,91,79,79,57,86,28,66,34,72,51,76,78,36,95,63,90,8,78,47,63,45,31,22,70,52,48,79,94,15,77,61,67,68);
$tri[99] = array(23,33,44,81,80,92,93,75,94,88,23,61,39,76,22,3,28,94,32,6,49,65,41,34,18,23,8,47,62,60,3,63,33,13,80,52,31,54,73,43,70,26,16,69,57,87,83,31,3,93,70,81,47,95,77,44,29,68,39,51,56,59,63,7,25,70,7,77,43,53,64,3,94,42,95,39,18,1,66,21,16,97,20,50,90,16,70,10,95,69,29,6,25,61,41,26,15,59,63,35);
$sumTri[0] = array(59);
for ($i=1; $i <= 99; $i++) {
for ($j=0; $j < ($i+1); $j++) {
$sumTri[$i][$j] = 0;
}
}
for ($i=0; $i < 99; $i++) {
for ($j=0; $j < count($tri[$i]); $j++) {
$tempsum1 = $sumTri[$i][$j] + $tri[$i+1][$j];
if ($tempsum1>$sumTri[$i+1][$j]) {
$sumTri[$i+1][$j] = $tempsum1;
}
$tempsum2 = $sumTri[$i][$j] + $tri[$i+1][$j+1];
if ($tempsum2>$sumTri[$i+1][$j+1]) {
$sumTri[$i+1][$j+1] = $tempsum2;
}
}
}
$maxSum = 0;
for ($i=0; $i < count($sumTri[99]); $i++) {
$sumTri[99][$i];
if ($sumTri[99][$i]>$maxSum) {
$maxSum = $sumTri[99][$i];
}
}
$answer = $maxSum;
$endTime = microtime(true);
echo "Answer: ",$answer,"\nTime: ",($endTime - $startTime),"\n";
// Answer: 7273
// Time: 0.012s