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This problem trains for: SAT-I, AMC-8, GMAT, AMC-10.

The Junk Pirates are now down to their last 162 biscuits. Trying to forget the hunger, they set to play a game where the biscuits are used for payment. In the first game, the First Pirate loses half of his biscuits to the Second Pirate. In the second game, the Third Pirate loses one third of his biscuits to the First Pirate. In the third game, the First Pirate loses 10 biscuits to the Third Pirate. In the fourth game, the Second Pirate loses 16 biscuits to the Third Pirate. After the fourth game, they notice that they have equal numbers of biscuits. How many biscuits did the First Pirate have at the beginning of the game?

Use backtracking. Start at the end of the game when each pirate has 54 biscuits and perform all the operations in reverse.

GameFirstSecondThird
4545454
3547038
2647028
1507042
01002042

The first pirate started with 100 biscuits.