A medium question on pigeonhole principle for P4–P5, 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 marbles in 2 colours, plenty of each, alike except for colour.
May takes them out one by one without looking.
What is the fewest she must take to be sure of 3 the same colour?
Show the hints (2)
💡Hint 1: With the worst luck, how many of each colour can she take and still not have 3 alike?
💡Hint 2: With 2 of every colour, how many is that? What happens with one more?
Worked solution
Have a go first, then read the solution step by step.
1.Worst luck: 2 of each colour, 2 × 2 = 4, still not 3 alike.
2.One more, whatever its colour, makes 3 of that colour: 4 + 1 = 5.
⚠️Common mistake: 2 × 3 = 6, which would give 3 of every colour.
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