Exercise · ZW-PIGEONHOLE-PRINCIPLE-010 · ★★★ Advanced
21 integers are chosen. At least how many are certain to end in the same units digit?
Choose one option.
Show answer
- B. \(3\)
Explanation
There are 10 possible digits and \(\lceil 21/10\rceil=3\). With 20 integers there could be just 2 per digit, but the 21st forces a third.
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 \(n>k\).
\[\left\lceil \dfrac{n}{k}\right\rceil\]
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