In the tradition of weighing puzzles, you have yet another batch of coins to sort. The only way to distinguish the coins is by their weights. This time there are nine coins. Three coins weigh 20g, three coins weigh 21g, and three coins weigh 22g.

You need to sort the coins by weight, but this time you must use an unusual three way scale. The scale operates as follows:

- Three weights must be placed on the scale for a meaningful result.
- If all three weights are equal, the scale will be in perfect balance.
- If one weight is lighter than the other two, the scale will show that weight is the lightest.
- If two weights are equal and are lighter than the third, the scale will indicate that scenario.

Examples:
Ex1: If A=30 B=30 C=30 then the scale will be in balance.
Ex2: If A=30 B=31 C=32 then the scale will indicate that A is the lightest of the three, but not tell which of B and C is lighter.
Ex3: If A=30 B=31 C=31 then the scale will indicate that A is the lightest of the three, but not tell that B and C are equal. (undistinguishable from Ex2)
Ex4: If A=30 B=30 C=31 then the scale will indicate that A and B are equal and less than C.

Using this three way scale, can you sort the coins in five weighings?

(In reply to Is 4 weighings possible? by Charlie)

No... In each weight we have 7 possible outcomes, in 4 weights we have 2400 possible outcomes.  But in each weight we are given a peice of information to helpl us solve the puzzle.  Your logic is good until the comparison of 2400 to 1680.  There are 2400 possible outcomes of 4 peices of information, there is 1680 possibilities for weights for the 9 coins.    If somehow it was given that  4 peices of information did in fact solve the puzzle for us then yes, 4 trials would work.  Otherwise we have 4 peices of information that will help us but not necessarily solve the puzzle.  In fact 5 is the lowest amount of weighings that solves and will work with any outcome on the weighings, if the coins are picked right.

Posted by james on 2005-09-13 09:40:49