1 8 15 22 29 36 43
2 9 16 23 30 37 44
3 10 17 24 31 38 45
4 11 18 25 32 39 46
5 12 19 26 33 40 47
6 13 20 27 34 41 48
7 14 21 28 35 42 49
In the 7x7 array given above, select six numbers from six cells simultaneously satisfying the following conditions:
- No two numbers chosen should belong to the same row;
- No two numbers chosen should belong to the same column;
- In the set of numbers chosen, each of the ten digits appears once and only once.
For example, if the numbers selected are 7,9,18,26,30 and 45 then this violates the given conditions as 9 and 30 belong to the same row.
No idea if this solution is unique, but one group of numbers that fits the bill would be 6 (1,6), 8 (2,1), 17 (3,3), 25 (4,4), 30 (5,2), 49 (7,7). The numbers in parentheses indicate each number's column and row, respectively; column 6 and row 5 are omitted.
As a starting point, note that for all ten digits to appear once in a group of six numbers, two of those numbers must be single-digit. Given restriction #2, this means that a solution must include either 8 or 9, along with one of the digits 1-7, which also means that neither of the first two columns may be omitted in any solution.
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Posted by Jyqm
on 2013-03-05 14:32:34 |
One solution
