GK 2019 Q10
10. Which of the following 4 × 4 tiles cannot be formed by combining the two given pieces?


Grey Kangaroo 2019, Question 10. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: E
When the two given pieces are joined together, any resulting square must have on its outside one row and one column, each of which have alternating black and white squares. Therefore tile E cannot be made. The diagrams below show how the tiles in options A, B, C and D can be made by combining the given pieces, confirming E as the only tile which cannot be made.

Solution © UK Mathematics Trust, from the GK 2019 solutions.