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UKMT Mathematical Olympiad for Girls, 2021

Combinatorics Difficulty 3.0 AMC 10/12 Prove it United Kingdom

Consider a $4 \times 4$ grid numbered 1 to 16 left to right then top to bottom. Tile A or Tile B is placed onto the grid so that it covers three adjacent numbers. In how many different ways can Tile B be placed onto the grid (the orientation of the tile may be changed) so that the sum of the uncovered numbers is a multiple of three?

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