Complementary counting

Sometimes counting what you do not want is far easier than counting what you do. Count everything, count the bad ones, subtract. Any question with the words at least or not is a candidate.

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Work through it

LearnWhat it is, how to spot it, a worked example, and where it goes wrong.
Practice — 3-point ladder2 problems. Three in a row finishes it.0/3 in a row · 0/2 solved
Practice — 4-point ladder2 problems. Three in a row finishes it.0/3 in a row · 0/2 solved
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-04Casework

Opens up

CNT-10Inclusion–exclusion with two sets CNT-11Counting with restrictions

In official papers

No indexed official paper question has been tagged with CNT-09 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.

See the papers indexed so far

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