Problem 3 · 2025 AMC 8
Medium
Arithmetic & Operations
total-then-dividedivision
Buffalo Shuffle-o is a card game in which all the cards are distributed evenly among all players at the start of the game. When Annika and 3 of her friends play Buffalo Shuffle-o, each player is dealt 15 cards. Suppose 2 more friends join the next game. How many cards will be dealt to each player?
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Answer: C — 10 cards each.
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Hint 1 of 2
More friends show up, but no new cards do. What's the one number here that stays exactly the same?
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Hint 2 of 2
The total number of cards is fixed. Find that total from the first game, then share it among the new, larger group.
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Approach: fixed total of cards, redistribute among players
- The deck doesn't grow when friends arrive — the total number of cards is the thing that stays fixed. Find it: 4 players × 15 cards = 60 cards.
- Now redeal that same 60 among 4 + 2 = 6 players: 60 ÷ 6 = 10 cards each.
- Why this transfers: in any "shared evenly" problem, hunt for the quantity that doesn't change (here, the total). Pin it down once, then it answers every version of the question.
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