947 views
1 votes
1 votes
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?

1 Answer

Best answer
1 votes
1 votes
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.
selected by

Related questions

0 votes
0 votes
0 answers
2
Debargha Mitra Roy asked Sep 26, 2023
175 views
Determine the geometric distribution for which the mean is 3 and variance is 4.
2 votes
2 votes
2 answers
4