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Always greater (Posted on 2007-04-14) Difficulty: 3 of 5
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!

    See The Solution Submitted by Federico Kereki    
    Rating: 3.5000 (2 votes)

    Comments: ( Back to comment list | You must be logged in to post comments.)
    Solution A boring game | Comment 5 of 6 |
    If N is odd, the first player always wins; if even, the second player wins... and, in fact, the game need not be more than one turn long!

      Posted by Old Original Oskar! on 2007-04-15 13:37:05
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