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Four Coins and Three Weighings (Posted on 2007-03-08) Difficulty: 3 of 5
You have four coins to sort with a standard balance scale. Their weights are 20g, 21g, 22g and 23g. Prove that there is no strategy which can guarantee sorting the coins with only three weighings.

  Submitted by Brian Smith    
Rating: 4.3333 (3 votes)
Solution: (Hide)
There are 24 possible ways for the weights to be assessed to the four coins. With three weighings there are only 27 possible outcomes. Four outcomes from all 27 possibilites involve two or three equal weighings. Therefore at least one of the 24 possible ways to sort the coins involves at least two equal, different weighings.

The only possible way for a weighing of the coins to balance is to have the 21g and 22g coin on one side and the 20g and 23g on the other side. With only one possibility for an equal, there cannot be 24 possible outcomes from the weighings.

Federico Kereki gives an information theory solution here.

Charlie gives a more thorough analysis here.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Some Thoughtsre: All things being equal **Look for the flip sideAdy TZIDON2007-03-10 17:25:04
Hints/TipsAll things being equalGamer2007-03-10 14:55:51
Hints/Tipsre: proof ..... not applicableAdy TZIDON2007-03-10 04:06:26
how to edit my postAdy TZIDON2007-03-10 02:50:11
Solutionit is possible!!!!Ady TZIDON2007-03-10 02:47:36
re(2): Information theory wayGamer2007-03-09 11:43:25
re: Information theory wayCharlie2007-03-09 09:50:07
SolutionInformation theory wayFederico Kereki2007-03-08 16:09:28
SolutionproofCharlie2007-03-08 15:46:14
Some ThoughtsAlmost a solution...Old Original Oskar!2007-03-08 15:17:12
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