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There are two groups of flowers. Group $A$ has $17$ flowers and Group $B$ has $13$ flowers. Cathy and Ivy want to play a game with these flowers. They will take turns to take flowers from the two groups. Each person can take any number of flowers from a group at a time. The person who takes the last flower in two groups will win the game. If Ivy starts the game first, who has the winning strategy? 
Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Game Strategy
Two groups of flowers are not equal. Thus, Ivy needs to take away 4 flowers from Group A and two groups will have the same amount of flowers. Then, Ivy will become the second mover and she has the winning strategy. 