Linear Combinations of 5 and 7: Lower Secondary Mathematics Competition Question

You are given two tiles, one has dimensions 1x5 units and the other is 1x7 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 12 using one 5 and one 7. You cannot make an area of 11 using just these two tiles.

The question is: what is the largest possible area that cannot be made using just the tiles 1x5 and 1x7?





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