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Combinatorics problem
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Consider the diagram. It shows 4 letters, which represent 4 contestants, who follow defined rules: 1. Each contestant is required to move once in each turn, with these turns being simultaneous for all contestants. 2. Each contestant can only move to the right in each turn, except if they are adjacent to a dotted line, in which case they can move to the connected square. 3. Each contestant can move through any dotted line only once, that is, they can only use a dotted line once during the entire game. 4. Contestants are eliminated if they end up in the same square, or if 2 contestants use the same dotted line at the same time. 5. All contestants who reach the last square on the right side will win, thus leaving the board on the next turn. Based on all of the above, and assuming that the contestants can communicate with each other and are always honest, so the game is not random, is there any way that they can all win? If not, What is the most optimal combination or combinations for the greatest number of contestants to win?

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6 months ago