Hidden Progressions
How many 3-element subsets of {1, 2, ..., 20} have the property that, when their elements are listed in increasing order a < b < c, they form an arithmetic progression (that is, b − a = c − b)? Give an integer.
Related problems & prerequisites
Worth solving first
- Eight Rooks 4.0/10
Source: Classic counting exercise in wide circulation; no traceable original source. Statement written for AxiomIQ.