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determine which of classes X_r, r \in {0, 1, 2\} is the largest, mod 3

Source: Indian Postal Coaching 2008 set 6 p6

May 25, 2020
combinatoricsnumber theoryremainder

Problem Statement

Consider the set A={1,2,3,...,2008}A = \{1, 2, 3, ..., 2008\}. We say that a set is of type r,r∈{0,1,2}r, r \in \{0, 1, 2\}, if that set is a nonempty subset of AA and the sum of its elements gives the remainder rr when divided by 33. Denote by Xr,r∈{0,1,2}X_r, r \in \{0, 1, 2\} the class of sets of type rr. Determine which of the classes Xr,r∈{0,1,2}X_r, r \in \{0, 1, 2\}, is the largest.
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