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King's Maths School

Challenge 446: Gingerbread Tiling

A loosely seasonal puzzle to round out the term!

Thanks to Jason F for another WMC puzzle!

Santa wants to tile the walls of this house with gingerbread pieces. Help him decide how to do the following!

For each part, you should explain (a) for what values of N it is possible, (b) an algorithm to follow when it is possible, and (c) a proof of when it is impossible.

(1) Tile an NxN wall with 2x2 and 1x3 gingerbread pieces.

(2) Tile an NxN wall with 3x3 and 2x3 gingerbread pieces.

(3) Tile a triangular wall of height N with 1x2 gingerbread pieces. (For example, a triangular wall of height 3 has 1 squares in the top row, 3 squares in the second row, and 5 square in the third row, with a vertical line of symmetry.)

Submit your solution

Please do send in your solution to this problem to weeklymaths@kcl.ac.uk You can scan or photograph your written work, or type your solutions. If this is your first weekly maths challenge solution, please include your year group and the name of the school you attend. We'll be happy to provide feedback on your solution, assuming that you are in year 11 or below. If you are older than this, we hope you enjoy trying the problems and reviewing your solutions against those we publish on the website.