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?

Thank you to pcbouhid for clarifying the problem, though truth be told, it was clarified in the problem all along.

I have an 11 move solution similar to Cory Taylor's.  I did read Cory's solution, though I'm not sure I understood all of it.  I tried it myself, but my approach was probably influenced by Cory's.

First, weigh block 1 vs 2.
If they don't balance, use this pair as a standard to weigh against the 9 other pairs.
If they do balance, weigh this pair against the next pair (3 and 4)

If 1,2 vs 3,4 doesn't balance, weigh 3 vs 4.
If 3 vs 4 doesn't balance, use this pair as a standard to weigh against the other 8 pairs.
If 3 vs 4 balances, use the pair 1 and 3 as a standard to weigh against the other 8 pairs.

If 1,2 vs 3,4 balances, weigh 1,2 vs 5,6, and then repeat the steps in the previous paragraph, except replace 3 with 5 and 4 with 6, and now there are only 7 pairs left.  If it balances again, use the next pair, and the next, and so forth.

If 1 vs 2 balances and 1,2 balances with all other pairs, then all the blocks are aluminum (since they can't all be duraluminum).

Posted by Tristan on 2005-06-07 18:53:12