Use complement counting when “at least one” is cumbersome.
National problems often present a calculation that looks tedious but has a clever shortcut. Mathcounts National Sprint Round Problems And Solutions
Page 7. Copyright MATHCOUNTS, Inc. 2024. All rights reserved. 2025 Chapter Sprint Round. 26. _____________ 27. _____________ 28. _ MATHCOUNTS Foundation MATHCOUNTS - AoPS Wiki Use complement counting when “at least one” is
We count possible triples ((A,B,C)) with (A \in [1,9]), (B,C \in [0,9]). For each (A,B), (C = 9k - 2S) must be between 0 and 9 inclusive. C)) with (A \in [1