#657335
Postby jfgw » April 1st, 2024, 10:43 pm
Spoiler
The matches have to be laid flat on the table. Does this preclude overlapping? If so, I am not sure if UncleEbenezer's method can be made to work, bearing in mind that squares have sides of equal length. This is an issue with the question, however — the four "squares" are not exactly square. This can be resolved by arranging the matches in the way that UncleEbenezer suggests but without leaving a tiny square in the middle.
I think that the intended solution could be very similar, however.
I think we have to ignore the match heads otherwise the shapes in the question are not quite squares, even with the slight rearrangement.
Pedantry aside, this would work:
The matches need to be arranged similarly to the photo in the question. The four middle matches should just touch on the corners, leaving a small square hole in the middle, i.e., so that the ends of the matches form the sides of the square. The outer matches need to be placed so that they just touch at the outer corners, and just touch (corner to corner) the middle matches.
Julian F. G. W.