其它
There are two groups of balls. Group $A$ has $585$ balls and Group $B$ has $590$ balls. DQ and Justin want to play a game with these balls. They will take turns to take balls from the two groups. Each person can take $1$ to $6$ balls from a group at a time. The person who takes the last ball in the two groups will win the game. If DQ starts the game first, does she have the winning strategy? 
Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Game Strategy
DQ needs to take the $590-585=5$ balls in Group $B$ which will make the two groups have the same amount of balls. Then, no matter how many balls Justin takes in a group, DQ will take as many balls as Justin took before in the other group. 