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.

(In reply to answer by I)

That solution requires knowing whether the fake is heavier or lighter. According to the problem, youknow its weight is "off," but you don't know in which direction. For the second and third weighings, you eliminated the unweighed coin and the coins in one pan, but how did you determine which pan?

Posted by TomM on 2002-10-23 10:27:31