In a pile, there are 11 coins: 10 coins of common weight and one coin of different weight (lighter or heavier). They all look similar.

Using only a balance beam for only three times, show how you can determine the 'odd' coin.

Open problem (i cannot solve this myself): how many more coins (with the same weight as the ten) can we add to that pile so that three weighing still suffices? My conjecture is zero, though my friend guessed that adding one is possible. The best bound we can agree upon is < 2.

I think I read somewhere that this can be done with 12 coins and still able to determine whether the last one is heavier or lighter than the others...

I worked out the solution Half-Mad gave but i couldn't figure out how to get all possibilities to show whether the odd coin was heavier or lighter...

Posted by Aeternus on 2002-10-11 04:38:29