The 12 Coins Puzzle

[Ephrium]

You are welcomed. I found how however, that I can only know which is the odd coin, but not whether it is heavier or lighter with two weightings of 5 coins. Hence to conform to the two criterion, 12 coins is the max.

[Tiberius]

Well look at that...I forgot to post the traditional solution!

Label the coins A, C, D, E, F, I, K, L, N, M, O, and T. Weigh them according to the following statement:

MA DO LIKE
ME TO FIND
FAKE COIN

i.e. weigh MADO vs LIKE, METO vs FIND, and FAKE vs COIN.

Draw up a table of weighings vs coins (so 3 columns and 12 rows) and put the results of each weighing (either tilts left, tilts right, or balances) into it. From this, you can tell which coin is the odd one, and whether it is heavy or light.

[jvwert]

Form three (3) main groups – each containing 1 and 3 coin sub-groups. Place one main group on each pan of a two pan balance – the third main group on the table. Observe the condition of the balance. This is the first weighing.

Rotate the 3 coin sub-groups (from pan A to the table, pan B to pan A, and from the table to pan B. Observe the condition of the balance. (second weighing).

If there is a change, it will identify the 3 coin group that contains the odd coin and its relative weight. In this case, clear the area of all other coins. Split this group into single coins, placing two on the pans of the balance. This willl be the third weighing and will identify the odd coin. We already know its relative weight. Problem solved.

If there is no change, one of the single coins (two of which are already on the pans of the balance) is the odd coin. In this case, rotate the single coins. This will be the third weighing an will identify the odd coin and its relative weight. Problem solved.

[Welsh cake]

I honestly can't see how you're supposed to isolate the odd coin from the other eleven whilst determining whether the coin is heavier or lighter, even through deductive reasoning. Looking at the probability of choosing the odd one out from the process of elimination, this impractical puzzle leaves no room for error. You'd need to conduct six measurements, not just three; under either presumption said odd coin is heavier or lighter.

I think I'll go and punish myself with a Rubik's cube now.

[Tiberius]

I honestly can't see how you're supposed to isolate the odd coin from the other eleven whilst determining whether the coin is heavier or lighter, even through deductive reasoning. Looking at the probability of choosing the odd one out from the process of elimination, this impractical puzzle leaves no room for error. You'd need to conduct six measurements, not just three; under either presumption said odd coin is heavier or lighter.

I think I'll go and punish myself with a Rubik's cube now.

The solution is here: http://atheistforums.org/thread-2838-pos...l#pid56224

[Alston]

Wow mathematical calculations...I always hate mathematics just because of i never get it in my mind..