Combinatorics · Counting · Residue classes · Binomial coefficients · Case analysis
How many three-element subsets \(\{a, b, c\}\) does the set
\[ A = \{19, 20, 21, \ldots, 98\} \]
have with the property that \(a + b + c\) is divisible by \(3\)?
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Serbian Regional Competition (Okruzno takmicenje) 1998, high school grade I, problem 1. The 1998 regional paper was not split into categories. Organized by the Mathematical Society of Serbia (DMS). Source