Professor Reginald laid 40 matches out on the table and explained the game to his colleague Kathy.

Each player in turn takes 1, 3, or 5 matches. The winner is the one who takes the last match. Kathy goes first and takes 3 matches.

Who do you think is going to win this game, Kathy or Reginald?

I'm going with Reggy here. We are subtracting odd numbers from an even number. Leaving one left over. Because Kathy went first after going back any forth Reggy will always be the one with the last pick. So Reggy will win.

ReplyDeleteReginald will win.

ReplyDeleteEvery turn an odd number of matches is subtracted. Thus, every

twoturns, an even number of matches are subtracted (two odd numbers will always add up to an even number). There will always be an even number of matches on Kathy's turn (after each player has had n turns - ie. 2n turns) and an odd number of matches on Reginald's turn (after 2n-1 turns). Since the players have to pick up an odd number of matches, Reginald is the only one who will ever be able to pick up all the matches.Lady and Charli kick major ass! we came up with the same answer intuitively but could not possibly have been able to explain why.

ReplyDeletekudos guys!

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.ero

If Reginald is the one who picks 5 matches per turn. Then, he's the winner.

ReplyDeleteThe one who pick first will always lose.

ReplyDeletefrom the combination I did, Reginald won. Though if Kathy were smart she would realize she can't win and ask to start over again with HIM going first then she would win :P

ReplyDeleteYou all have it right (nice work!).

ReplyDeleteBut if the person who picks first will always lose the question becomes how can you make the game fairer?

reginald won. visit mine http://unscrambletheletters.blogspot.com/

ReplyDeleteIntroduce choice of picking even numbers of matches~ XD

ReplyDelete