THE CROSS OF CARDS.—solution

There are eighteen fundamental arrangements, as follows, where I only give the numbers in the horizontal bar, since the remainder must naturally fall into their places.

5 6 1 7 4
3 5 1 6 8
3 4 1 7 8
2 5 1 7 8
2 5 3 6 8
1 5 3 7 8
2 4 3 7 8
1 4 5 7 8
2 3 5 7 8
2 4 5 6 8
3 4 5 6 7
1 4 7 6 8
2 3 7 6 8
2 4 7 5 8
3 4 9 5 6
2 4 9 5 7
1 4 9 6 7
2 3 9 6 7

It will be noticed that there must always be an odd number in the centre, that there are four ways each of adding up 23, 25, and 27, but only three ways each of summing to 24 and 26.

 

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