A Strategy For Solving The Forged Coin Problem
Edward J Robinson [Collins HS]
 28 March 2000

There are twelve coins, one of which is forged. The forged coin is either lighter or heavier than the others. By using at most three weighings on a balance scale, find the forged coin and determine whether it is heavier or lighter than the other coins.

Divide the twelve coins into three groups of four, groups A,B,C.

First weighing

Place group A on the left and place group B on the right. Set group C aside. If the balance is equal then the forged coin is in group C. If the balance tends to the left, then the forged coin is either in group A or B. If the forged coin is in group A, then it is heavier; if the forged coin is in group B, then it is lighter. If the balance tends to the right, then the forged coin is either in group A or B. If the forged coin is in group A, then it is lighter; if the forged coin is in group B then it is heavier.