The first solution was so wrong I was compelled to answer this question correctly.
The original poster needs to have his posting privileges SEVERELY limited for the sake of limiting stupid activites whenever possible.
Question: You are given 12 coins. One of them is heavier or lighter than the rest. Identify this coin in just three weighings
Solution: Number the coins 1 through 12 and divide them coins into 4 sets of 3...
There are multiple comparison sets possible. This is an acceptable template to find a few of them. (This template is NOT definitive, there are other solutions that don't follow this template)
Compare (set 1 & 1st coin from set 4) against (set 2 + 2nd coin from set 4) Compare (set 1 & 2nd coin from set 4) against (set 3 + 1st coin from set 4) Compare (1st coin from each set) against (3rd coin from each set)
A more concise example:
Compare 1 2 3 10 against 4 5 6 11 Compare 1 2 3 11 against 7 8 9 10 Compare 1 4 7 10 against 3 6 9 12
Each weighing can have 3 possible outcomes: Left Heavy, Right Heavy, or Balanced (L,R or B)
Build a truth table to interpret outcomes...many outcomes are not possible. Note: THE TABLE VALUES ARE DERIVED FROM THE CHOSEN COMPARISON SETS!
outcome: fake coin: l l l 1 is heavy r r r 1 is light l l b 2 is heavy r r b 2 is light l l r 3 is heavy r r l 3 is light r b l 4 is heavy l b r 4 is light r b b 5 is heavy l b b 5 is light r b r 6 is heavy l b l 6 is light b r l 7 is heavy b l r 7 is light b r b 8 is heavy b l b 8 is light b r r 9 is heavy b l l 9 is light r l r 10 is heavy l r l 10 is light l r b 11 is heavy r l b 11 is light b b r 12 is heavy b b l 12 is light
There are multiple comparison set possibilities, each with their own comparison table solution.