Exercise · ZW-PIGEONHOLE-PRINCIPLE-003 · ★☆☆ Basic
How many cards from a 52-card deck (4 suits) must be drawn at minimum to guarantee two of the same suit?
Choose one option.
Show answer
- B. \(5\)
Explanation
With 4 cards they can all be of different suits; the fifth forces a repeated suit (4 boxes, 5 objects).
Review the concept: Pigeonhole principle
If \(n\) objects are placed in \(k\) boxes, some box holds at least \(\lceil n/k\rceil\) objects, and in particular two when \(n>k\).
\[\left\lceil \dfrac{n}{k}\right\rceil\]
More practice problems: pigeonhole principle
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- ZW-PIGEONHOLE-PRINCIPLE-009 Seven numbers are chosen from the set \1,2,dots,12\. Which statement is always true?