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| A Magic Rectangle Problem (Posted on 2006-07-16) |
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Fill a 10x8 matrix with 80 distinct integers between 1 and 160 (both numbers inclusive) so each of its ten rows adds up to 640, and each of its eight columns adds up to 800.
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Submitted by K Sengupta
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Rating: 3.5000 (2 votes)
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Solution:
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(Hide)
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As rightly pointed out by Steve Herman and Dej Mar, this problem admits of more than one solution.
One of the arrangements satisfying conditions of the problem is given below:
| 1 | 11 | 131 | 121 | 119| 109 | 69 | 79 |
| 3 | 13 | 133 | 123 | 117| 107 | 67 | 77 |
| 5 | 15 | 135 | 125 | 115| 105 | 65 | 75 |
| 7 | 17 | 137 | 127 | 113| 103 | 63 | 73 |
| 9 | 19 | 139 | 129 | 111| 101 | 61 | 71 |
|151| 141 | 21 | 31 | 49 | 59 | 99 | 89 |
|153| 143 | 23 | 33 | 47 | 57 | 97 | 87 |
|155| 145 | 25 | 35 | 45 | 55 | 95 | 85 |
|157| 147 | 27 | 37 | 43 | 53 | 93 | 83 |
|159| 149 | 29 | 39 | 41 | 51 | 91 | 81 |
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