Berkeley Math Circle: Monthly Contest 7 #0hr6
Berkeley Math Circle: Monthly Contest 7Hard
From module Sum Formulas for Powers
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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 / monovariantsCounting two waysSums and products
Problem
Problem:
Eight friends, Aerith, Bob, Chebyshev, Descartes, Euler, Fermat, Gauss, and Hilbert, bought tickets for adjacent seats at the opera. However when they arrived they mixed up their seats:
- Bob sat in his assigned seat,
- Chebyshev sat two seats to the right of Gauss' assigned seat,
- Descartes sat one seat to the left of Fermat's assigned seat,
- Euler sat four seats to the left of Hilbert's assigned seat,
- Fermat sat five seats to the right of Descartes' assigned seat,
- Gauss sat one to the right of Euler's assigned seat,
- Hilbert sat three seats to the left of Aerith's assigned seat. In whose seat did Aerith sit?