[Game] Picking Matches

• CoolMyth

  13 Feb 06, 01:06

  Game: http://www.coolmath-games.com/matches/index.html
  
  To play: Press "Start". Enter a number between 2 and 60 and click on "Accept".
  
  Rules: You will always start first. You are to pick between 1 to 3 matches at your turn and your opponent will do likewise.
  
  Objective: Whoever pick the last match is the loser.
  
  Question: For any number of matches that you can chose to start with, how do you play so that you will win everytime?
• CoolMyth

  13 Feb 06, 01:16

  Since you always go first, there are some numbers where you will definitely lose.
  
  So, rephrasing the questions:
  
  i)Identify the number of the matches at the start of the game, such that you will definitely lose the game?
  
  ii)How do you win in those that you can win?
• mystiv

  13 Feb 06, 19:49

  dunnoe
  
  start with 5 you confirm lose
  
  just make sure you pick the number of matches till you leave 5 for the computer
• CoolMyth

  13 Feb 06, 19:54

  Originally posted by mystiv:

  dunnoe
  
  start with 5 you confirm lose
  
  just make sure you pick the number of matches till you leave 5 for the computer

  Got formula one.
• finoq

  13 Feb 06, 20:03

  Coolmyth Coolmath
  
  um what happened....i anyhow press suddenly they say I win
• finoq

  13 Feb 06, 20:08

  ha i sorta know...i chose 17, then when I took 1, he took3. I took 3 he took 1. I took 2 he took 2. Since we take in sets of 4s, when the 4th set finishes I left 1 as 17-(4X4)=1 which means I lose...
• finoq

  13 Feb 06, 20:11

  hm...but then, when I chose 10, and I pick 1 match all the way the 1st time I won...but the 2nd time I lost...
  
  1st time
  
  10
  
  -1
  -3(com)
  -1
  -3(com)
  -1
  
  win
  
  2nd time
  
  10
  
  -1
  -1(com)
  -1
  -2(com)
  -1
  -3(com)
  
  lose
• CoolMyth

  13 Feb 06, 20:16

  Here's the answer anyway:
  
  i)In cases where the number of matches, n = 4k + 1, where k is any integer, since you start first, you will always lose.
  
  Let's say, you picked p matches, the computer will pick q matches such that p + q = 4, so no matter what you do, you will end up having to take that last match and lose.
  
  The numbers in these cases are 5, 9, 13, 17, 21..... etc.
  
  ii)In cases where the number of matches, n is not in the form n = 4k + 1. You can always win by first choosing a number of matches such that the remaining number, m is in the form 4k + 1.
  
  For example, let's say you start with 30. The greatest number closest to 30 in the form 4k + 1 is 29 (k = 7), so you chose 1 match first.
  
  Hence, for every p matches the comp picked up, take q matches such that p + q = 4. You will win the game definitely.
  
  Try it and see for yourself!
• mystiv

  13 Feb 06, 20:21

  i see
• finoq

  14 Feb 06, 00:07

  i knew it, i could never win with 17