NRICH: Tiled Floor

This tiled floor has 109 purple tiles. How many tiles are there altogether?

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.

Age 11 to 14


Math Topics
Algebra & Pre-Algebra, Patterning & Sequencing
Middle School, High School, Educator
6th Grade, 7th Grade, 8th Grade, 9th Grade

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