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: Fair Game (spoiler) by Steve Herman)

You are absolutely right, however " they are powers of 2" is slightly erroneous definition, better wording would be 1:2:4 ratio or similar.

I was going (and still will) mention this fact in my official solution.

Posted by Ady TZIDON on 2015-08-22 02:37:05