Impressed by Mario's answer, Quacky drags him into a chamber for a challenge.Cham- ber has two cells, A and B, with m dogs in one cell and n dogs in another. He also has a magical Dog Killer, which allows him to kill any number of dogs from any one of the cells or kill equal number of dogs from both the cells. For example, he can kill 4 dogs from A or 7 dogs from B or 3 dogs from both A and B. For winning the challenge, Mario must be the one killing the last dog. However, he realises that Quacky also has the same magical Dog Killer, and would take turns with him in order to try and get him killed.Quacky asks Mario to do the first move.How many dogs should Mario kill in his first move if cell A houses 12 dogs and B 15 dogs so that he can survive?

Impressed by Mario's answer, Quacky drags him into a chamber for a cha

1.	Impressed by Mario's answer, Quacky drags him into a chamber for a challenge.Cham- ber has two cells, A and B, with m dogs in one cell and n dogs in another. He also has a magical Dog Killer, which allows him to kill any number of dogs from any one of the cells or kill equal number of dogs from both the cells. For example, he can kill 4 dogs from A or 7 dogs from B or 3 dogs from both A and B. For winning the challenge, Mario must be the one killing the last dog. However, he realises that Quacky also has the same magical Dog Killer, and would take turns with him in order to try and get him killed.Quacky asks Mario to do the first move.How many dogs should Mario kill in his first move if cell A houses 12 dogs and B 15 dogs so that he can survive?
Answer» 10 14 16 12 Solution :If you have the first move to MAKE, what will be your stretagy? One thing is for sure that you can not always win. For example in a configuration (1,2) it is impossible for you to win no matter what move you make. In a sense (1,2) is a losing state. Your job is to find out WHETHER given configuration is a winning state or not and if it is a winning state, what will be the sequence of moves that will lead you to victory. There cannot be any losing state which has a difference of 1 since they can be brought to (1,2) which is a losing state and there is no other losing state with one of the 2 numbers i.e 1,2 since they can be brought tolosing state. Next (3,5) is a losing state and then (4,7) (5,9) (6,11) (8,14) (10,17) (11,19) (12,21) (13,23)(15,26) From (12,15), the only LOOSING state you can bring to is (4,7) which REQUIRES Mario to kill 16dogs( 8 from each)

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