There are 10 non distinguishable balls and one of these has different weight(one does not know whether it is weigh more or less than others). One can use scales 3 times to compare their weight. You can easily show that starting with comparing 2 sets of 3 balls always gives the result, that is, you can always find the one with different weight using scales 3 times. Details are omitted.
But if the number of balls are more than 10, then it seems impossible to find the one. I want to prove this. When a chance to use scales remains only 1 time, we should know that 2 balls contain the one or that 3 balls contain the one with its weight known. But when chances remain 2 times, situation becomes complicated. I need your help.
