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 Information theory way by Federico Kereki)

I don't quite understand your statement about "if you weigh two coins against two coins, in just ONE case you get an "equal" result".

If you weigh AB vs CD, the sequences ADBC, ADCB, DABC, DACB will all produce "equal" results.  And, of course if you weigh AC vs BD or AD vs BC, different sequences will produce the "equal" result, so I don't see how this generalization fits in.

Posted by Charlie on 2007-03-09 09:50:07