An easy question on pigeonhole principle for P3–P4, with a step-by-step solution, diagrams and the answer. Common in the Hua Xia Cup's P3 to P6 qualifying rounds and finals. The trick is to imagine the unluckiest case.
The question
All 11 oranges go into 3 baskets, any number in each basket.
However they're placed, some basket is sure to hold at least how many?
Show the hints (2)
💡Hint 1: To keep every basket as light as possible, how should you place them?
💡Hint 2: Share them out evenly first: what is 11 ÷ 3? Is anything left over?
Worked solution
Have a go first, then read the solution step by step.
1.11 ÷ 3 = 3 remainder 2.
2.Put 3 in each basket; the 2 left over must go somewhere, making that basket 4.
3.So some basket holds at least 3 + 1 = 4. Common mistake: answering 3, forgetting the leftover oranges must go somewhere.
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