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Three coins (Posted on 2015-08-20) Difficulty: 3 of 5
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.

See The Solution Submitted by Ady TZIDON    
Rating: 2.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Hints/Tips re: question | Comment 2 of 10 |
(In reply to question by Charlie)

my interpretation of MG text:

the coins belong to the table, and after a round of games they stay on the table.

Claiming a coin should be understood as designating a token i.e. identifying a  player. The amounts lost are paid out of the pocket and the coins remain "table's property"

Sample single game and result:

A's choice being  a quarter,  B by default  has a 50c and 100c coins.

If the  quarter was the only HEAD,  then A WINS   1.5 $ by "taking all three coins".

I had some problems with the text, copied here verbatim,   and reached my conclusions after reading    the original answer.

Have fun....

  Posted by Ady TZIDON on 2015-08-20 15:00:40
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