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The q-round Rényi-Ulam pathological liar game with k lies on the set [n] := {1,..., n} is a 2-player perfect information zero sum game. In each round Paul chooses a subset A ⊆ [n] and Carole either assigns 1 lie to each element of A or to each element of [n]\A. Paul wins if after q rounds there is at least one element with k or fewer lies. The game is dual to the original Rényi-Ulam liar game for which the winning condition is that at most one element has k or fewer lies. Define F*k(q) to be the minimum n such that Paul can win the q-round pathological liar game with k lies and initial set [n]. For fixed k we prove that F*k (q) is within an absolute constant (depending only on k) of the sphere bound, 2q/(qk); this is already known to hold for the original Rényi-Ulam liar game due to a result of J. Spencer.

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Journal of Combinatorial Theory. Series A

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