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GWhD(\(v\))s, or Generalized Whist Tournament Designs on \( v \) players, are a relatively new type of design. GWhD(\(v\))s are (near) resolvable (\(v,k,k-1\)) BIBDs. For \( k = et \), each block of the design is considered to be a game involving \( e \) teams of \( t \) players each. The design is subject to the requirements that every pair of players appears together in the same game exactly \( t-1 \) times as teammates and exactly \( k-t \) times as opponents. These conditions are referred to as the Generalized Whist Conditions, and when met, we refer to the (N)RBIBD as a (\( t, k \)) GWhD(\(v\)). When \( k = 10 \), necessary conditions on \( v \) are that \( v \equiv 0, 1 \pmod{10} \). In this study, we focus on the existence of (\(2,10\)) GWhD(\(v\)), \(v \equiv 1 \pmod{10}\). It is known that a (\(2,10,9\))-NRBIBD does not exist. Therefore, it is impossible to have a (\(2,10\)) GWhD(\(21\)). It is established here that (\(2,10\)) GWhD(\(10n+1\)) exist for all other \(v\) with at most 42 additional possible exceptions.