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