When in 39 coins, put 13 coins in one side and 13 coins in another.
1. If the two sides are equal, the game is impossible and you have to refresh.
2. If one side is heavier and the other is lighter, it is solvable:
Move 9 coins from the lighter side to the heavier side, move 9 of the coins from the heavier side away, and put 9 of the other coins to the lighter side. The heavier side becomes side A, and the lighter side becomes side B.
1. If the two sides are equal, this means one of the 9 heavier coins put away is fake. Place 3 of them on one side and 3 of them on the other. If one side is heavier the fake coin is there, if the two sides are equal the fake coin isn't there. Then place 1 of the fake suspects on one side and 1 on the other.
2. If side A is heavier, this means that either the 4 coins in side A may be fake (heavier) or the 4 coins in side B may be fake (lighter). On side A place 1 of the heavier fake suspects and 3 of the lighter fake suspects, on side B place 1 of the lighter fake suspects and 3 good coins.
de NOT Novel Games2