Exercise · ZW-PIGEONHOLE-PRINCIPLE-001 · ★☆☆ Basic
A group has 13 people. What can be stated with certainty about their birth months?
Choose one option.
Show answer
- A. At least two were born in the same month
Explanation
There are 13 people and only 12 months (boxes), so by the pigeonhole principle some month repeats. Nothing guarantees that every month is used or that exactly two share one.
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-005 100 people are grouped by birth month (12 months). At least how many are certain to share some mont…
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- ZW-PIGEONHOLE-PRINCIPLE-009 Seven numbers are chosen from the set \1,2,dots,12\. Which statement is always true?