MaplePrimes - answers and comments on Question, How many nails can be hammered into the chessboard with Maple?

Manual solution

Kitonum — Fri, 16 Nov 2012 23:24:30 Z

We have 64 points with coordinates (x_i, y_j), where x_i=1..8, y_j=1..8 . The right answer is 16 points (2 points in each row and each column):

4 4 8 8 2 2 6 6

3 3 7 7 1 1 5 5

For brevity, only the second coordinates are specified. The first column contains the points for which the first coordinates equal to 1 and so on.

Obviously, if the number of points is greater than 16, at least three points lie in one line.

This problem was discussed at the Russian site http://dxdy.ru/topic62965.html

I think the solving this problem in Maple is not easy - it takes too long time.

Markiyan Hirnyk — Sat, 17 Nov 2012 00:05:48 Z

Thank you for the answer. It would be interesting to find a smaller set having this property, say a set with 10 elements, by Maple.

PS. Does there exist a solution of different type?

Kitonum — Sat, 17 Nov 2012 00:56:52 Z

To find a smaller set having this property is easy without Maple - just remove any 6 elements of the given set of 16 elements.

I do not know of another type of solutions than those that can be obtained apparent transformations: reflections and rotations.

Markiyan Hirnyk — Sat, 17 Nov 2012 01:18:37 Z

The question is how to produce such a set with Maple. Here is my attempt to find the three-element subsets.