probability

Question

Alice and Betty play a game where Alice goes first. They each say a distinct integer from 1 to 15 (inclusive). The first person to say an integer which we summed with a previously spoken integer, gives the value of 16, will lose the game. Who will win the game?

Comments

Alice gets a first chance then he can choose any number from (1-15) but betty will choose  from numbers except from which on addition with previously chosen with alice's digit,we will get 16.

suppose,sequence is like this:

alice   betty

9          2

8          10

11         3

4           7

5           6

12         13

14         15

1                 //alice has no other coice but to choose 1,so (15+1) = 16,hence alice looses and betty wins

 

BUT now consider this scenario:-

Alice     Betty

10          3

7            4

11          6

12          13

15          5

1           14

9            2

8            8   //here beety has no other coice but to choose 8 and hence,it makes up 16.and in this case alice wins

 

so,how can we decide that whether alice will win or betty wil win??

Answer 1

Betty will always win.

See how.

As there are 15 numbers, Alice will always be chossing last. Now, consider what will happen during the last 3 choose operations.

Lets say Alice chooses any number at the 3rd place from last . Now, there are 2 nos left.

Now, there is a possibility that Betty chosses a number due to which she losses or choose a number due to which Alice is forced to choose a specific number at last . Obviously she takes the second option due to which Betty either wins or draws the game but never loses.

Comments

i got your point..thanks a lot