Exercise · ZW-PIGEONHOLE-PRINCIPLE-005 · ★☆☆ Basic
100 people are grouped by birth month (12 months). At least how many are certain to share some month?
Choose one option.
Show answer
- C. \(9\)
Explanation
\(\left\lceil \dfrac{100}{12}\right\rceil=\lceil 8.33\rceil=9\).
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?