Problem 8 · 2023 AMC 8
Medium
Logic & Word Problems
sum-constraintcasework
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Answer: A — 000101.
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Hint 1 of 2
Don't reconstruct who-beat-whom. Each round, the 4 players split into 2 matches — so every round produces exactly 2 wins. That fixed total is your lever.
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Hint 2 of 2
Read the table by column instead of by row. Each column (round) must sum to 2 across all four players, so Tiyo's entry is just 2 minus the other three.
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Approach: each round's wins sum to 2
- The shortcut: you don't need the matchups. Every round, four players pair into two games, so exactly 2 wins (and 2 losses) get handed out — meaning every column of the table sums to 2.
- So add Lola + Lolo + Tiya down each round: 2, 2, 2, 1, 2, 1.
- Tiyo fills the gap to 2 each round: 0, 0, 0, 1, 0, 1 = 000101. This transfers: when each ‘round’ has a fixed total, an unknown row is just total minus the known rows — column thinking beats casework.
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