Berkeley Math Circle Monthly Contest 5 #0ho0
Berkeley Math Circle Monthly Contest 5Hard
From module Strategy and Write-up Structure
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Understand the scale
Scale
0.5: Easiest math competition problems, often solvable even for early middle school students without experience.
1: Problems strictly for beginners, often at a moderate middle school level.
1.5: Problems for stronger beginner students, on the level of the middling problems in most middle school contests.
2: For motivated beginners, harder questions from the previous categories.
2.5: More advanced beginner problems, hardest questions from previous categories.
3: Early intermediate problems that require more creative thinking.
3.5: Tougher early intermediate problems that consistently stretch into higher-level creative thinking or conceptual knowledge.
4: Intermediate-level problems.
4.5: Upper intermediate problems approaching the upper bound for non-invitational sprint math competitions.
5: More difficult AIME problems or simple proof-based Olympiad-style problems.
6: High-level AIME-styled questions or introductory Olympiad-level questions.
7: Tougher Olympiad-level questions, may require more technical knowledge.
8: High-level Olympiad-level questions.
9: Expert Olympiad-level questions.
9.5: The hardest problems appearing on Olympiads which the strongest students could reasonably solve.
10: Historically notorious problems, generally unsuitable for even very hard competitions because they are exceedingly tedious, long, and difficult.
Invariants / monovariantsGames / greedy algorithms
Problem
Problem:
Alice and Bob play the following game on the whiteboard. First, Alice writes an odd number in binary on the board. Then, beginning with Bob, the players take turns modifying the number in one of two ways: subtracting from it (preserving the binary notation), or erasing its last digit. When the whiteboard is blank, the last player to have played wins. Which player has a winning strategy?