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After an attempted breakout at Folsom State Prison, the warden lines the prisoners up for a headcount. (Assume the warden counts correctly and that no prisoners switch positions or leave/escape during either headcount.) When the warden counts from left to right, Gurby is the 20th prisoner counted, but when the warden counts from right to left, Gus is the 20th prisoner counted. How many prisoners are lined up for the headcount?

(1) There are 13 prisoners between Gurby and Gus.

(2) The total number of prisoners is odd



VERITAS OFFICIAL EXPLANATION



The crucial question is whether, from the warden's point of view, Gurby is to Gus's left or Gus's right. If Gurby is to the left of Gus, then there are \(19\) prisoners before Gurby, \(13\) between Gurby and Gus, and \(19\) after Gus, for a total of \(19+1+13+1+19 = 53\) prisoners. If Gurby is to the right of Gus, then there are \(5\) prisoners before Gus, \(13\) between Gus and Gurby, and \(5\) prisoners after Gurby, for a total of \(5+1+13+1+5 = 25\) prisoners. Even together, both scenarios are possible, so we can't determine the total.
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