# Euler Problem 11

In the 20×20 grid below, four numbers along a diagonal line have been marked in brackets.

``````08  02  22  97  38  15  00  40  00  75  04  05  07  78  52  12  50  77  91  08
49  49  99  40  17  81  18  57  60  87  17  40  98  43  69  48  04  56  62  00
81  49  31  73  55  79  14  29  93  71  40  67  53  88  30  03  49  13  36  65
52  70  95  23  04  60  11  42  69  24  68  56  01  32  56  71  37  02  36  91
22  31  16  71  51  67  63  89  41  92  36  54  22  40  40  28  66  33  13  80
24  47  32  60  99  03  45  02  44  75  33  53  78  36  84  20  35  17  12  50
32  98  81  28  64  23  67  10 [26] 38  40  67  59  54  70  66  18  38  64  70
67  26  20  68  02  62  12  20  95 [63] 94  39  63  08  40  91  66  49  94  21
24  55  58  05  66  73  99  26  97  17 [78] 78  96  83  14  88  34  89  63  72
21  36  23  09  75  00  76  44  20  45  35 [14] 00  61  33  97  34  31  33  95
78  17  53  28  22  75  31  67  15  94  03  80  04  62  16  14  09  53  56  92
16  39  05  42  96  35  31  47  55  58  88  24  00  17  54  24  36  29  85  57
86  56  00  48  35  71  89  07  05  44  44  37  44  60  21  58  51  54  17  58
19  80  81  68  05  94  47  69  28  73  92  13  86  52  17  77  04  89  55  40
04  52  08  83  97  35  99  16  07  97  57  32  16  26  26  79  33  27  98  66
88  36  68  87  57  62  20  72  03  46  33  67  46  55  12  32  63  93  53  69
04  42  16  73  38  25  39  11  24  94  72  18  08  46  29  32  40  62  76  36
20  69  36  41  72  30  23  88  34  62  99  69  82  67  59  85  74  04  36  16
20  73  35  29  78  31  90  01  74  31  49  71  48  86  81  16  23  57  05  54
01  70  54  71  83  51  54  69  16  92  33  48  61  43  52  01  89  19  67  48

``````

The product of these numbers is 26 × 63 × 78 × 14 = 1788696.

What is the greatest product of four adjacent numbers in the same direction (up, down, left, right, or diagonally) in the 20×20 grid?

``````

In [1]:

grid = """
08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48
"""

L = list(map(int, grid.split()))

def f(i,j):
if i<0 or i>19 or j<0 or j>19:
return 0
return L[20*i+j]

p = 1
for i in range(20):
for j in range(20):
p = max(p, f(i,j)*f(i,j+1)*f(i,j+2)*f(i,j+3))
p = max(p, f(i,j)*f(i+1,j+1)*f(i+2,j+2)*f(i+3,j+3))
p = max(p, f(i,j)*f(i+1,j)*f(i+2,j)*f(i+3,j))
p = max(p, f(i,j)*f(i+1,j-1)*f(i+2,j-2)*f(i+3,j-3))
print(p)

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70600674

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In [ ]:

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