Make three piles of 122 coins. Weigh two against each other (use #1). if one is heavier, it's the pile you want. If not, it's the third pile. you've narrowed it down by a third
cut into two piles of 41 and one pile of 40. Weight the piles of 41 against each other (#2). The heavier pile has the coin. If they balance, it's the pile of 40.
make two piles of 20 (if you have one left over, that's fine). Weigh them against each other (#3). The heavier pile has it. If they balance, then you had a coin left over and you're done. Other wise you're down to 20 coins.
Split into two piles of 7 and one pile of 6. Weigh the piles of 7 against each other (#4). The heavier pile has it. If they balance, the pile of 6 has it.
split it into two piles of 3 and a pile of 1. Weigh the piles of three against each other (#5). The heavier pile has the coin in it. If they balance, the coin left out is it and you're done.
At this poing you're either done or have 3 coins left. Weigh two of the coins against each other (#6). the heavier coin is it. If they balance, the odd coin out is it. Either way you're done in 6 weighs.
But it only takes one more weigh to split it in half. each time, sometimes with an odd one out.
