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(3): question
by Ady TZIDON)
I myself did not answer the puzzle's question, but Steve Herman did: Regardless of which coin is owned by one of them, and the other two coins owned by the other player, it's a fair game--the answer is it doesn't matter.
I did not give the answer, as it is given in the book chapter referenced; I hadn't worked it out myself except in retrospect to verify the answer given in Gardner's book, which I had to look at to see the actual quotation, as your's was not verbatim as claimed.
Posted by Charlie
on 2015-08-22 07:40:37