Twenty metal blocks are of the same size and external appearance; some are aluminum, and the rest are duraluminum, which is heavier.

Using a pan balance to determine how many blocks are aluminum, what is the minimum number of weighings to be done?

(In reply to re(5): between... by Cory Taylor)

The thing is, I thought I had also mentioned 2^20-2 and 3^N, which would only correspond to the way I first interpreted the problem.  Perhaps I only considered saying that, or was on the verge of saying it.  That's what happens when I overthink my comments.

In any case, you are correct, I do not have a way to beat your 11 weighing solution.  Though 3 is the theoretical minimum, I expect the best solution would not be nearly so good.  If I thought differently earlier, it was only because I'm so used to these problems working out so that the theoretical minimum is in fact achievable.

Posted by Tristan on 2005-06-07 06:28:57