Grid Investigations Notes

1) In the 12 match grid it is not possible to make the diagonals both have 4 heads.

Here is an arrangement in which the two diagonals are equal with 2 heads in both. So the possible values for the diagonals are 2, 5, 8,

2) With 6 in each row and column it is possible to make arrangements with 4, 6 or 8

in the diagonals.

3) In the 40 match Grid it is possible to equalise rows, columns and diagonals with 8 in each.

Keeping the rows and columns equal the diagonals can be equalised with any number of matches between 2 (shown here) and 14 in both the diagonals.

A good method of transforming patterns while maintaining constant matches in rows and columns is to turn pairs of opposite facing matches so that

becomes