There were $$8$$ cups on the table with the sides up,  If you can only turn $$6$$ at a time,  Can it be done to make all the cups face down at the end? 
Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Operational Problem->Turning Mugs over
To make all the $$8$$ cups face down, it only needs to turn them over with odd times, and 6 of them can be turned at a time, so it can be done. 