# Question 4

## Question 4

Question 4 :

Impressed by Mario's answer, Quacky drags him into a chamber for a challenge. Chamber 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?

(a) 10 (b) 14 (c) 16 (d) 12

Impressed by Mario's answer, Quacky drags him into a chamber for a challenge. Chamber 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?

(a) 10 (b) 14 (c) 16 (d) 12

**TECHNOTHLON**- Admin
- Posts : 39

Join date : 2016-07-19

## Re: Question 4

**Answer is sure 16**.Note that both 2,1 and 5,3 are winning pairs.So if he eats 8 dogs from both then

4 and 7 dogs are left

If Quacky eats 1 dog from the room with 4 dogs then it becomes 3

and mario can convert the no.of dogs in room b to 5

If he eats 2 or 3 dogs from room A then Mario can covert no. of dogs in second room to 1 or 2 Making him win

So U can make cases like this and observe he will always win

**The answers.org**- Guest

## My opinion

The answer must be 14. This can be easily found out by using a method known as 'Winning Position Method". The way is by removing 7 and 7 from both the sides.

Reference: Mathematical Circles(*Russian Experience).

Reference: Mathematical Circles(*Russian Experience).

**Aryan Mundada**- Guest

## Come on!!

The answer is 10. The turtle is not a fool (as you may have guessed while solving the paper) and so will always try to win, and in all the cases except 10, Mario loses. Try this game out with matchsticks with some wise person and get the answer for yourself!

**SidRis**- Guest

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