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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: 4.0000 (2 votes)

    Comments: ( You must be logged in to post comments.)
      Subject Author Date
    A Combinatorics ApproachGamer2007-04-16 01:32:28
    SolutionA boring gameOld Original Oskar!2007-04-15 13:37:05
    SolutionSolution to the second questionDej Mar2007-04-14 16:06:04
    SolutionsolutionCharlie2007-04-14 15:12:01
    SolutionAnswer to the first questionDej Mar2007-04-14 13:57:00
    Top limit?brianjn2007-04-14 11:39:28
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