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 "Thus, if AB=CD AB>CD, the cases ..."
you mean " /...... if AB=CD AC>BD etc"
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.......