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Counting arithmetic triples

EasyProbabilityCombinatorics~3m

How many increasing 33-term arithmetic progressions can be formed using the integers {1,2,…,20}\{1, 2, \dots, 20\}? (For example 3,7,113, 7, 11; the three terms must be distinct.)

Show hints (2)+
  1. An AP is fixed by its start aa and common difference dd, not by picking 3 values.
  2. For each dd there are 20−2d20-2d valid starts; sum over d=1,…,9d=1,\dots,9.

Answer

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90

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Asked at: Timed Mental-Math & Sequences, Game-Based Aptitude

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