Can you sum me out?
The rules of this game are simple:
1. Numbers 1, 2, 3... 9 are arranged in a row. At every turn, each player chooses a number and adds it to all the previously chosen numbers.
2. The player who gets to 15, by summing any 3 of his chosen numbers, wins.
For example
Turn 1:
Me 5
You 9
Me 8
You 2
Me 3
You 4
You win (9+2+4=15)!
If you win, I will give you triple the money. If I win, I keep your money. If neither wins, the pot is split. To give you the advantage of winning, I will let you choose your turn - that is, you can choose to play first or second!
Would you want to play with me?
Clue: This problem can be reduced to a certain well-known game played by us all during boring classes!
1. Numbers 1, 2, 3... 9 are arranged in a row. At every turn, each player chooses a number and adds it to all the previously chosen numbers.
2. The player who gets to 15, by summing any 3 of his chosen numbers, wins.
For example
Turn 1:
Me 5
You 9
Me 8
You 2
Me 3
You 4
You win (9+2+4=15)!
If you win, I will give you triple the money. If I win, I keep your money. If neither wins, the pot is split. To give you the advantage of winning, I will let you choose your turn - that is, you can choose to play first or second!
Would you want to play with me?
Clue: This problem can be reduced to a certain well-known game played by us all during boring classes!
posted by littlecow at 12/14/2005 10:41:00 AM
7 Comments:
This comment has been removed by a blog administrator.
If the game is to get to exactly 15, then neither player can ever win if the other player plays right. The play should be to select (15-x), where x is the score for the other player right now, if it is not yet chosen. If it is already chosen, then no problem. The other person can't win anyway.
@~a~: :)
@raju: your answer is not complete. for example, A and B play. A chooses 1. Now B should choose 15-1=14 according to your algorithm but 14 does not exist. Your algo needs a bit of fine tuning. See the new clue in the question!
Even if 14 is not available, you choose some number(maybe the highest available), because your opponent cannot choose 14 either when it is his turn. It becomes a series of checks'la chess.
There is no winner if you play it right. So both players should play not to lose.
@raju, grenade: you both are right. raju got the solution for the poorly worded problem and grenade is right about the rule. Rule 2 should read:
Any 3 of the numbers you have chosen add to 15. Now give it a shot!
it is like a game of tic-tac-toe. the 9 numbers can be arranged in a 3x3 matrix such that the diagonals, rows and columns add to 15. after that, it's basically a game of tic-tac-toe, with each person taking turns. if played right, the game always ends in a draw, whoever starts.
@lenscrafter: right on, arni. you get full points and raju gets 0.5.
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