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Tiled Floor

Age 11 to 14 Short
Challenge Level

In Andrea's house, all floors are square, and covered with square tiles.

Tiles along the diagonal are purple, and the other tiles are white, as shown in the diagram.

There are 109 purple tiles on the bathroom floor.

How many tiles are there altogether on the bathroom floor?

This problem is adapted from the World Mathematics Championships
You can find more short problems, arranged by curriculum topic, in our short problems collection.