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Tiled Floor

Age 11 to 14 Short Challenge Level:

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

Each tile along the diagonal is purple, and the other tiles are white, as shown in the diagram.

There are 109 purple tiles on the square 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.