mathschallenge.net

Problem

A kitchen floor is to be tiled in the following way,

If the kitchen measures 15 tiles x 25 tiles, how many white tiles will be needed?

Solution

The floor is made up of a 2x2 repeating pattern,

A 15 25 floor will fit 7x12 repeating blocks (14x24 tiles). The "end" lines will be all white.

So there will be 7 12 = 84 grey tiles.

Hence there will be 15 25 84 = 374 84 = 291 white tiles.

What about a kitchen measuring m n tiles?