Playing quarters with the devil
The devil has you captured and he agrees to leave you only if you win a game with him in playing quarters. The devil says "We both take turns in placing quarters on a table and the one who cannot place any more quarters looses". The devil also adds that there are no overlapping of the coins allowed. Now, what should your strategy be to win against the devil?Level: Medium
posted by Karthik Nagaraj at
6:03 PM
8 Comments:
Let x*y be the area of the table. Let r be the diamater of the coin and pi*r*r its area. if floor(x*y/r) is odd, then you start placing the coin first and you will place it last. If floor(x*y/r) let the devil begin the game so that you can end the game by being the last person.
You are not given the dimensions of the table - you dont even know if it going to be rectangular or circular until the game starts. But even then if you are going to consider the area, then what the about the area that is between 4 coins that touches one coin? Then in your case shouldn't the area of the coin be taken as a square (2r * 2r) instead of a circle. You are leaving out that small amount of area that cannot be used. You would somehow need to compensate for that right? I'm afraid the answer is not correct. Is there any way that a particular strategy will ensure that you win?
is the number of quarters limited? If so, then the chap can win if he has more quarters than the devil :).
oh ok, the strategy would be to start placing the quarters if there are an odd number of quarters and to allow the devil to start if the number is even.
The coins are unlimited and the only limitation is the number of coins the table itself can hold without overlapping, which of course you do not know before hand. Coming to whether it is odd/even, I dont think it really matters - as already said the # of quarters are unlimited and even if it were limited it will be more than what the table can hold and also you are not allowed to count them. So the answer is not correct.
Bobach writes:
I offer this not as a solution, but in the spirit of brainstorming to help others come up with a solution.
My instinct says I play first and I place the quarter in the geometric center of the table. Then I place my next coin at the midpoint of the line between my latest coin and the devil's last coin.
For the first 3 trivial cases. When the table is only big enough for:
1 coin - I win
2 coins - by hogging the center, there is no place around me where the devil can play. I win.
3 coins - by taking the center, there is the devil chooses one of the other 2 places and I get to play where the 3rd quarter can go.
Bobach,
Good attempt at getting to the solution. But there is one thing I dont understand - "Then I place my next coin at the midpoint of the line between my latest coin and the devil's last coin." Why would you want to place your next coin between the center of your latest coin and the devil's last coin? I can seem to understand what you trying to do here but a little more explanation can help for inviting more brainstorming. Good one - you are almost there so lets see more action...
Moot time is up guys - Bobach has got it almost right but some slight midifications. Maybe he/she meant it that way:
The idea is that the devil is very intelligent and he will try to outwit you in placing the coins by copying your placements. What this means is that if you place a coin somewhere on the table, the devil will place the coin on the opposite side in the same line as yours (mirror image) keeping some position as the mirror. So what is the strategy you need to adopt to overcome this intelligent thinking of the devil?
You say that you want to go first and you place the coin right in the geometric middle on the table. Now, the devil places the coin someplace, you just place your coin in the mirror image position keeping the central coin you placed as the mirror. So all the placements will be in accordance with the central coin. The devil will definitely loose in this type of playing.
So, Bobach, I can give you credit for this as you cracked the basic funda in the puzzle. Good thinking and nice way to go!
This puzzle is SOLVED!
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