Activity 31: Problems and Puzzles

You will have noticed as you have looked at the images and photographs of some of the rooms in the interior of the building that quite wide use is made of tiling on the floors.

These tiles are of different shapes and patterns. The easiest tiles to fit together are probably the square shapes.

Here a floor is being tiled with 25cm square tiles. The tiles are being laid, starting in one corner with one square and then attaching tiles around the two open sides of the tile.

The tiles are then laid in surrounding rows as in the diagram until the floor is covered:



Count up the numbers of tiles in each surrounding row and work out the total tiles used.

Complete this table

Row	Tiles	Total Tiles
1	1	1
2	3	4
3	5	9
4
5
6
7

Do you notice anything about the numbers in the second and third rows of the table?