Nim-Style Counting Game to 100
Two players take turns picking a number from $\{1, 2, \dots, 10\}$. A running total starts at $0$, and each pick is added to it. The player whose pick causes the total to reach or exceed
00$ wins. Player 1 goes first.
What is the winning strategy for Player 1? Specifically:
1. What should Player 1's first move be?
2. What are the "safe" totals Player 1 should aim to leave after each of their turns?
3. How should Player 1 respond to any move by Player 2?
Open the full interactive solver, hints, and worked solution →