Exercise · ZW-PIGEONHOLE-PRINCIPLE-002 · ★☆☆ Basic
30 marbles are distributed into 4 boxes. What is the largest number that is guaranteed to be in some box at least?
Choose one option.
Show answer
- C. \(8\)
Explanation
It is guaranteed that \(\left\lceil \dfrac{30}{4}\right\rceil=\lceil 7.5\rceil=8\). With 7 in each box only 28 would fit.
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?