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A tournament design, \({TD}(n, c)\), is a \(c\)-row array of the \(\binom{n}{2}\) pairs of elements from an \(n\)-set such that every element appears at most once in each column and there are no empty cells. An interval balanced tournament design, \(\text{IBTD}(n, c)\), satisfies the added condition that the appearances of each element are equitably distributed amongst the columns of the design. We settle the existence question for all \(\text{IBTD}(n,c)\)s by showing that they can be constructed for all admissible parameters and discuss the application of \(\text{IBTD}\)s to scheduling round robin tournaments fairly with respect to the amount of rest allocated to each participant.