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Game Theory 6.0/10

Race to 100

Two players start at 0 and alternately add any integer from 1 to 10 to a running total. Whoever brings the total to exactly 100 wins. The first player wins with optimal play. What number should the first player bring the total to on the first move?

Related problems & prerequisites

Worth solving first

Source: Classic subtraction game, a standard entry point to Nim-style analysis. Statement written for AxiomIQ.