A drunken soldier, starting at an intersection O in a city which has square blocks, staggers around a random path trailing a taut string. Eventually, he stops at an intersection (after walking at least one block) and buries a treasure. Let θ denote the path of the string from O to the treasure. Letting N, S, E and W stand for a path segment one block long in the indicated direction, so that θ can be expressed as a sequence of such letters, say θ =NNESWSWW. (Note that NS, SN, EW and WE cannot appear as the taut string would be rewound). After burying the treasure, the soldier walks one block further in a random direction (still keeping the string taut). Let X denote this augmented path, so that X is one of θN, θS, θE and θW, each with probability ¼ . You observe X and are then to find the treasure. Show that if you use a reference prior p(θ) ∝ 1 for all possible paths θ, then all four possible values of θ given X are equally likely. Note, however, that intuition would suggest that θ is three times as likely to extend the path as to backtrack, suggesting that one particular value of θ is more likely than the others after X is observed (due to M. Stone).