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. 
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? 
Yes, she can take $5$ balls from group $A$ at first. 
Yes, she can take $3$ balls from group $B$ at first. 
Yes, she can take $6$ balls from group $A$ at first. 
Yes, she can take $5$ balls from group $B$ at first. 
No, she doesn\textquotesingle t have winning strategy. 