The maximum number of coins for the solution is 3. This is basically what you arrive at when deriving the odd coin in a group of 12 ,allowing only 3 weighings, the maximum number for a solution is 3. Bottom line is that step 1) taking 1/3 of the coins on each pan and leaving 1/3 off. If they balance then step 2) divide those previously left off again into 1/3 on each pan and 1/3 off. 3) You will continue this until you are down to 3 coins. Then 1 on each pan , if they balance then the one left off is the odd coin. A) Now if at any time the number of coins is not evenly divisible by 3 ,then the left over coins go in the pile left off. B) If at any time during the early stages the pans do not balance , you will remove the right pan coins and divide the left pan into half placing 1/2 on each pan...they balance ,then the odd is obviously in the group removed from the right pan and start again at step 2) Now if they do not balance repeat B)