Combinations of Small Tiles: Upper Primary Mathematics Competition Question

You are given two tiles, one has dimensions 1x2 units and the other is 1x5 units.

You have as many of each tile as you need. You are asked to tile different areas using only these two tiles.

For example, you can make an area of 10 using just two 5s. You can make an area of 14 using two 5s and two 2s or with seven 2s.

Two questions

a) Which whole numbers cannot be made using just these two tiles?

b) In how many different ways can you make the number 30?




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