You are presented with a set of 90 coins, appearing identical.
Actually, 89 of them are identical, but one has a different weight.
Using balance scales you have to find the odd coin,
paying $10 each time you use the scales.

What is the maximal (i.e. the worst case) cost to accomplish it?

One out of 121 is possible with 5 weighings!  Use Brian Smith's excellent method, but have a 121st coin that is not involved in any weighings.  If his first 5 weighings all balance, then the 121st coin is the odd one.  Of course, we do not know whether it is lighter or heavier, but that was not required.

Posted by Steve Herman on 2015-12-19 19:20:20