There are $7$ water glasses, all facing up. You need to turn exactly $2$ glasses over in each time. Is it possible to turn all $7$ of them upside down after several moves? 
Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Operational Problem->Turning Mugs over
You have to flip a cup an odd number of times to turn it over.  To make all the $7$ cups face down, you have to make an odd number of flips.  Each time you flip exactly $2$ cups, the total number of flips is an even number of times.  Hence it is impossible. 