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
There are lots of socks in 3 colours, plenty of each, alike except for colour.
Ming takes them out one by one without looking.
What is the fewest he must take to be sure of two the same colour?
Show the hints (2)
💡Hint 1: With the worst luck, what colours could the first few be?
💡Hint 2: The worst case is one of each colour. How many is that?
Worked solution
Have a go first, then read the solution step by step.
1.Worst luck: the first 3 are one of each colour, no two alike yet.
2.The next one must match one of them: 3 + 1 = 4.
⚠️Common mistake: answering 2. With luck 2 is enough, but the question asks to be sure.
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