Extremal / worst-case counting

Some questions ask for the largest or smallest number that can be arranged, or how many are needed to guarantee an outcome. You have to argue on both sides: build an example that achieves the number, and explain why nothing better is possible.

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LearnWhat it is, how to spot it, a worked example, and where it goes wrong.
Practice — 3-point ladderNo problems written at this tier yet.Nothing written at this tier yet
Practice — 4-point ladderNo problems written at this tier yet.Nothing written at this tier yet
Practice — 5-point ladder4 problems. Three in a row finishes it.0/3 in a row · 0/4 solved
Skill quizFinish every ladder that has problems first.Finish the ladders above first

Before and after

Needs first

CNT-17The pigeonhole principle

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Nothing yet. No other skill in the Atlas lists this one as a prerequisite.

In official papers

No indexed official paper question has been tagged with CNT-18 yet. The index grows one paper at a time, and it records only question numbers, point values and our own skill tags — never the problems themselves.

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