CEMC Banner

Problem of the Week
Problem A
Tricky Tiles

Escher is planning to use tiles to create a border on his kitchen wall. The border will be formed by a row of single tiles. He has selected the first 8 tiles he plans to use. He has numbered them in the order of a pattern he wants to appear, from left to right. The pattern repeats every few tiles, and we can see the repetition in the first 8 tiles in the picture.

What will the 9th tile look like?

What will the 15th tile look like?

Eight tiles labelled 1 through 8. Tile 1 has a blue arrow pointing right and a white arrow pointing left. Tile 2 has a blue arrow pointing up and a white arrow pointing down. Tile 3 has a blue arrow and a white arrow both pointing right. Tile 4 has a white arrow pointing up and a blue arrow pointing down. Tile 5 is identical to tile 1, tile 6 is identical to tile 2, tile 7 is identical to tile 3, and tile 8 is identical to tile 4.