Two players play a game in which they alternate calling out positive integers ≤ N, according to:

The first player must always call out odd numbers.

The second player must always call out even numbers.

Each player must call out a number greater than the previously called number (except, obviously, the very first time).

The player who cannot call out a number loses.

How many different possible games are there? And, if we count a turn each time a player calls out a number, how many different K-turns games are there?

Note: the game is not very fun to play (why?) but the puzzles are interesting!

There are an infinite number of games as there are an infinite number of positive integers, but the number of different games can be expressed as that of the Fibonacci sequence --
where N = 1, 2, 3, 4, 5, 6, ...
the number of different games are 1, 1, 2, 3, 5, 8,....

 

Posted by Dej Mar on 2007-04-14 13:57:00