Question

Question No. 3
Abag contains 30 marbles Two players Aand B play the following game. They take out any under arbetade the
one to take marbles out of the bag is the winner After a few rounds there are 22 marbles entre
ambos
should he choose to eventually win the game?​

Answer 1

Given : A bag contains 30 marbles. Two players A and B play the following game. They take out any number of marbles between 1 to 7 in alternate turns from the bag . The last one to take the marbles out the bag is the winner. After a few rounds there are 22 marbles left in the bag.

To find : If it is B's turn, how many marbles should he choose to eventually win the game?

Solution:

Let say B take out  n Marbels  Then Marbles left = 22 - n Marbles

Now A can take any number from 1 to 7 and then

B can take any number from 7 to 1 to make it 8

Same process can be repeated again to take out 8 marbles

Hence total 16 marbles taken out and B take out the last marble    

22 - n = 8 + 8

=> 22 - n  = 16

=> n = 6

B should choose 6 marbles to eventually win the game

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