Discussion
A school has 100 students distributed among 1st to 10th standards.
Based on this, which one of the following statements is always correct?
Answer: A
The statement that is always true is There are at least 10 students who belong to the same standard.
This is the pigeonhole principle. If every one of the 10 standards had at most 9 students, the school could hold at most \(10 \times 9 = 90\) students. There are 100, so at least one standard must have 10 or more.
The other statements can fail. All 100 students could be in one standard, so a standard may be empty, and the 10th standard may hold more than 10. Equally, the 6th to 10th standards could hold all 100 students, leaving fewer than 50 in the 1st to 5th standards.
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