Three coins are lying on a table: a quarter, a half dollar, and a silver dollar. You claim one coin, I’ll claim the other two, and then we’ll toss all three.
A coin that lands tails counts zero, and a coin that lands heads wins its value
(in cents, 25, 50, or 100) for its owner.
Whichever of us has the larger score wins all three coins. If all three coins land tails then we call it a draw and toss again.
Which coin should you claim to make the game fair — that is, so that each of us has an expected win of zero?
Source: Martin Gardner, “Charles Addams’ Skier and Other Problems,” in Wheels, Life and Other Mathematical Amusements, 1983.
(In reply to re(4): question
Following your post, I make public the puzzle and enclose an abridged version of the solution.
I also provide exact reference of my source (had no reason to doubt its exactness).
If you have access to the original book, please Email the text with the solution, if it causes you no extra effort
I'd like to compare the versions re ambiguity, since both I and perplexus solvers felt that some assumptions needed to be added.
I have no hard feelings to the law rating someone declared,
after all it is not my puzzle.
Still, the result is really surprising.