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TSA 2022 · Question 43 · Optimisation

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In a game, players take it in turns to place tokens onto squares of a grid. The squares on the grid are coloured white and grey. When a player places a token they score one point for every token on an adjacent square (either horizontally or vertically). For every adjacent square that is white an extra point is scored. The diagram below shows a position in one game. The number on each square shows the number of tokens currently placed on that square:

Question diagram

What is the maximum number of points that could be scored when the next token is placed on the board?