Question 28
A grid sheet of paper of size $7 \times 7$ squares is given, together with an equally large plastic grid template on which some squares are green and the others are transparent. If the template is placed on the sheet of paper so that the sides of the template coincide with the sides of the paper, the grid pattern on the template coincides with the grid pattern on the paper. If we choose any square of the paper and colour it red, then the template can be placed on the paper so that its sides coincide with the sides of the paper and the red square of the paper is covered by one of the green squares of the template (before that, the template may be rotated arbitrarily and, if necessary, turned over to its back side). At least how many squares of the template are green?