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.

(In reply to All things being equal by Gamer)

By  "Thus, if AB=CD AB>CD, the cases ..."

you mean       " /...... if AB=CD AC>BD  etc"

  **********please edit

Charley,

I agree -   you are right.

However, since 4  different coins may be divided

into 2 subsets of 2  in 3 ways, there is 1 to 3 chance of getting

no balance (equality) in my  2 first steps, thus defining  the

heaviest and the lightest coin-  so enabling to assign 2nd and 3rd

places to the remaining coins,

e.g.  AB>CD , AC<BD  ===> B=23 C=20

and step 3. will be A vs D  , IF=A>D A=22   D=21

Looking for the flip side of the coin-sorting job

we will be fully successful in over 33% of the cases.

All in all- I liked the problem.......

 

 

 

Posted by Ady TZIDON on 2007-03-10 17:25:04