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        riddles >> medium >> square tile - either at center or next to boundary
        
(Message started by: gkwal on Jul 16^th, 2007, 9:31pm)

Title: square tile - either at center or next to boundary
Post by gkwal on Jul 16^th, 2007, 9:31pm

A 7 by 7 square is made up of 16 (1 by 3) tiles and 1 (1 by 1) tile. Prove that the 1 by 1 tile lies either at the centre of the square or adjoins one of its boundaries.

Title: Re: square tile - either at center or next to boun
Post by rmsgrey on Jul 17^th, 2007, 9:32am

I can go one better and prove there are only [hide]9[/hide] places it could be, all of which, apart from the central square, are on the boundary.

The key is the intermediate stage, which establishes [hide]17[/hide] possible squares.