Exercise · ZW-PIGEONHOLE-PRINCIPLE-008 · ★★☆ Intermediate
A list has 1000 distinct Spanish words. Using 26 initial letters, how many words with the same initial can be guaranteed?
Choose one option.
Show answer
- B. \(39\)
Explanation
\(\left\lceil \dfrac{1000}{26}\right\rceil=\lceil 38.46\rceil=39\).
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?