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platodog
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 Re: FAUSTIAN ROUND TABLE COIN GAME   « Reply #25 on: Jul 24th, 2005, 6:17pm » Quote Modify Remove

Wow! After reading your responses I fear that my answer is quite unintellectual, nonetheless, I propose as follows:

 hidden: Put the quarter on the table (or place the quarter on the ground), then flip the table upside down so the quarter is sandwiched between the ground and the table surface.  Since the table is upside down no more quarters can be placed on its surface.

Any thoughts?
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towr
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 Re: FAUSTIAN ROUND TABLE COIN GAME   « Reply #26 on: Jul 25th, 2005, 4:26am » Quote Modify

What's to stop the devil from flipping the table back?
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River Phoenix
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 Re: FAUSTIAN ROUND TABLE COIN GAME   « Reply #27 on: Jul 25th, 2005, 7:21am » Quote Modify

If the devil puts a coin levitated at a slant, just slide your coin under his and keep going.

The trouble is if he puts a coin down which whips around the table like an electron at infinite speed, knocking all your quarters off before they hit the surface.

Just don't look back.. and under NO circumstances should you eat the pomegranate.
 « Last Edit: Jul 25th, 2005, 7:25am by River Phoenix » IP Logged
Jayant Chauhan
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 Re: FAUSTIAN ROUND TABLE COIN GAME   « Reply #28 on: Jul 25th, 2005, 8:05pm » Quote Modify Remove

Well, with all the Lateral thinking you guys have done, I think its the fact that the packing of quarters is gonna tend to be hexagonal no matter what happens, the only deciding factor beingthe first move. The cases:
1) First player places the coin at the center, that makes the total no. of coins that can go onto the table as odd, hence the first person can manage to win,

2) First player places the coin newhere else, which results in an even number of coins, though it could still be even if the second player goofs up, who in our case is the DEVIL HIMSELF, so that ain't possible.

SO thats how it is done I suppose, no tilting and cheating
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Dr Irvine
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 Re: FAUSTIAN ROUND TABLE COIN GAME   « Reply #29 on: Sep 6th, 2005, 2:28pm » Quote Modify Remove

The symmetry solution contains an implicit assumption that you are not allowed to move coins that have already been placed on the table.  Nowhere in the problem is it stated that you cannot move already placed coins. If the devil is allowed to move coins, then there certainly exist tables on which an even number of coins can be placed (e.g. a table whose radius is exactly the diameter of a quarter).
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Icarus
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 Re: FAUSTIAN ROUND TABLE COIN GAME   « Reply #30 on: Sep 6th, 2005, 5:26pm » Quote Modify

Gareth Pierce suggested nudging the coins around on the first page, and I pointed out that there are tables which allow only an even number of coins (using the exact same example as yours).

But as I also pointed out in the same post, the devil is a shifty creature and will twist the rules to his advantage, so you need to be sure before the start that you know exactly what is allowed, and what isn't. Or else, attempt all twists first, so the devil must state the restrictions (and therefore live by them).

But alas, he is known as the "Prince of Lies", so even if you win, your fate is still surely bad.
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Citizen
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 Re: FAUSTIAN ROUND TABLE COIN GAME   « Reply #31 on: Jul 24th, 2006, 1:48pm » Quote Modify

The rule set as put to you by the devil:
- take turns putting quarters down
- no overlapping allowed
- the quarters must rest on the table surface
- the first guy who can't put a quarter down loses

Possible twists -
1. Starting first, put down all of your coins; this guarantees you're not the first guy who can't put a quarter down
2. Stretch the first quarter to a size such that it covers the entire table (remember, this is hell - fire and brimstone abound.  you could get the metal hot enough)
3. Nick a quarter from the devil - if he runs out first then he can't put a quarter down (assumes you start with equal piles and the table can accomodate all coins)
4. Take the coins, buy a tiny table with room for just one coin and put your quarter there
5. Give your quarters to the poor beggar so he can buy some food - God will be so moved by your generous sacrifice that he'll rescue you from the Devil and hell

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Icarus
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 Re: FAUSTIAN ROUND TABLE COIN GAME   « Reply #32 on: Jul 24th, 2006, 6:18pm » Quote Modify

(There's really no point in hiding at this stage in a thread. Hiding is only useful if you are posting a legitimate solution near the beginning of the thread. This prevents other people from seeing the answer before they get the chance to think about the problem themselves. But anyone reading here is well passed that and is sure to read everything anyway.)

on Jul 24th, 2006, 1:48pm, Citizen wrote:
 1. Starting first, put down all of your coins; this guarantees you're not the first guy who can't put a quarter down

On Nick's turn, he places a single coin of his down, then says "your turn".

Quote:
 2. Stretch the first quarter to a size such that it covers the entire table (remember, this is hell - fire and brimstone abound.  you could get the metal hot enough)

You quickly recognize that Satan has simply failed to provide any foundry tools (inhospitable fellow that he is). Attempts to stretch the coin with your hands and feet quickly leave them too burned to manipulate anything. Satan looks at you and says "I guess that means you are unable to place a coin, now doesn't it?
Quote:
 3. Nick a quarter from the devil - if he runs out first then he can't put a quarter down (assumes you start with equal piles and the table can accomodate all coins).

You slyly drop your purloined coin into your sack, amazed at how easy it was to put one over on ol' beelzebub. But something nags at your brain, and after considerable thought, it finally hits you: there was no "clink" when you dropped in the coin. In dread you open the bag and look in. There is your purloined coin, all alone. Bub's bag is looking suspiciously full, as he gives you a large grin. Wasn't there something about him also being the Prince of thieves?

Quote:
 4. Take the coins, buy a tiny table with room for just one coin and put your quarter there.

"Very clever!", says Lucifer, "indeed, I never specified that this was the table we would both use. I must bow to such brilliance and allow it. So, that is your table, where all of your moves are made, and this is mine, where all of my moves are made.

Quote:
 5. Give your quarters to the poor beggar so he can buy some food - God will be so moved by your generous sacrifice that he'll rescue you from the Devil and hell

The Devil starts laughing uproarously at your generous gesture. "Fool!", he says, "has it escaped your notice that this is Hell? Did you not know that everyone here was sent here to be punished, even the beggars? Indeed, your beggar friend was a greedy miser on earth who never shared with anyone, and his punishment here was to experience the other end. Did you expect God, who knows your motives, to be moved by this false mercy?"
 « Last Edit: Jul 24th, 2006, 6:25pm by Icarus » IP Logged

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 Re: FAUSTIAN ROUND TABLE COIN GAME   « Reply #33 on: Jul 25th, 2006, 10:00am » Quote Modify

Icarus - thanks for the warm welcome to Wu Riddles.  Nothing like having your ideas smashed by a moderator.

j/k

Actually, I should have seen the inherent contradiction between my first and third solutions.  On the other hand, I don't think the rules said anything about whether you could lift coins from the table and place them back down again.  Would be a possible response after the devil's counter to my first solution - though that would lead to a game of infinite length (on the other hand, you'd be helping out a lot of poor souls to whom the devil might otherwise turn his attention  ).

What I don't like about the symmetry solution (which seems most popular) is that, like my scenarios, it is just that: a scenario.  Why would the devil play with a symmetrical table?  Furthermore, assuming he did, why would he then let you start first?  He's gotta know some math, afterall.

I'm looking for some sort of infallible response to this problem - just not sure what it is yet.

BTW - Just to introduce myself.  I'm Tom from Canada.  I've lurked in this forum for about a week and I gotta say, I like it.

edited for typos
 « Last Edit: Jul 25th, 2006, 10:02am by Citizen » IP Logged
Icarus
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 Re: FAUSTIAN ROUND TABLE COIN GAME   « Reply #34 on: Jul 25th, 2006, 12:31pm » Quote Modify

There is a very common theme in fantasy stories about someone who is offered something they very much want, only to discover (or at least the reader discovers) that the one offering twists the reward so that while it technically matches the desired thing, it actually is just opposite the person's real desires.

For example, two stories by Orson Scott Card that I remember: In the first, a woman at the end of an ideal day runs into a peddler who brings up fears as to what the future holds, and then offers to let her have ideal days like this one for the rest of her life. She agrees, and ends up reliving that same day over and over in her mind, regardless of what actually is happening around her. The result destroys the lives of her family, whose wife and mother no longer has any attachment to their real lives.

The second involved a woman who is granted 3 wishes by a magical dragon. She wishes that her farm would alway provide enough to feed her family. So the dragon flies off and devours her family, then returns and informs her that now no matter how much her farm produces, it will always be enough to feed her family.

This riddle is a similar set-up. No matter how you try to limit things, this is the Father-of-Lies you are dealing with. He will twist things to your disadvantage. At the least, he is a liar, so how likely do you think it would be that he will let you free even if you did win?

Anyway, I must thank you for the fun challenge of figuring out how all your alternatives could go wrong. And, to be even handed:

on Jul 25th, 2002, 5:03am, Viorel Canja wrote:
 The right explanation is that by placing a coin in the center the resulting free table surface has the property that any valid coin position has a coresponding valid position that is simetrical to the center of the table. If the devil can place a coin then you can place a coin in the associated simetrical position.

You lean back after placing the first coin, confident that even though you can't spell "symmetrical", you at least know what it means, and how to apply it here for certain victory. You close your eyes for a moment to savor the upcoming victory only to hear a crunching sound. You open your eyes to see a quarter-sized hole in one edge of the table. The evil one smiles and says "these matches always make me a little hungry". Then he places his coin exactly opposite the hole.

on Aug 1st, 2002, 12:23pm, Salem wrote:
 lay the table on it's side, place your quarter on the new top of the table (which was the side of the table). This is the only place a quarter will stay

After careful work, you succeed in balancing a coin on the top of the table edge. You were a little surprised that the Prince of Darkness did not object when you turned the table on its side, but he just set back and smiled. (Oh, how you hate that smile!) Relieved that you have pulled it off, you lean back and .... notice the table foot sticking straight up, with just enough room to balance a second coin. His grin deepens...

on Oct 4th, 2004, 5:51am, Squigs wrote:
 If you want to cheat, simply refuse to put a coin down.  Since he has to wait until you put yours down, the devil will be unable to put his down.

"Ah, a sneaky one!", says the Deceiver, "Indeed, I cannot move if you don't. But then, you cannot move without releasing me from this condition, and letting the game go on to its inevitable conclusion. Which means that you are first unable to move on your turn!"

on Jul 24th, 2005, 6:17pm, platodog wrote:
 Put the quarter on the table (or place the quarter on the ground), then flip the table upside down so the quarter is sandwiched between the ground and the table surface.  Since the table is upside down no more quarters can be placed on its surface.

The Father of Lies growls "I thought you were educated, yet you don't understand simple instructions. The coins, I said, are to rest on the table surface, not the table surface to rest on the coin! The penalty for misplay is forfeiture of the game!"

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I wonder: Which is larger
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towr
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 Re: FAUSTIAN ROUND TABLE COIN GAME   « Reply #35 on: Jul 25th, 2006, 1:02pm » Quote Modify

I suppose, to have a chance to win, you ought to get a fair arbiter to judge the game. God would be my choice.

Anyway, the devil hasn't the power to let you into heaven, so just repent.
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zbudde
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 Re: FAUSTIAN ROUND TABLE COIN GAME   « Reply #36 on: May 27th, 2013, 6:14am » Quote Modify

Put your quarter on the table, then throw the table, quarter and all, into the nearest pit of fire and brimstone, or destroy it by some other means. The rules did not state that the quarter must STAY at rest on the table surface, so after placing it, destroy the table, no more next turn for the devil.
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Iz
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 Re: FAUSTIAN ROUND TABLE COIN GAME   « Reply #37 on: Jun 17th, 2013, 3:28pm » Quote Modify

My take:

You place a quarter on the table and tell the devil, "Ok, I'll let you know when my turn is over."

Since you have placed a quarter on the table and your turn is still going, you have won the game. The Devil cannot place a quarter until you are done with your turn, and you choose to make your turn last infinitely.

Ask for ice cream on the way to heaven.
 « Last Edit: Jun 17th, 2013, 3:37pm by Iz » IP Logged
yevvi
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 Re: FAUSTIAN ROUND TABLE COIN GAME   « Reply #38 on: Jun 21st, 2014, 6:44pm » Quote Modify

Not sure if this solution has been already posted, here my take on it:

1st move: put a coin straight at the center (centers of coin and table coincide)
After that:

Every time devil puts a coin, we put coin symmetrically opposite to that coin relative to the center of the table (center of our coin is same distance from the center of the table as center of devils coin and 3 of these centers form straight line).

This way, no matter where devil puts the coin, we know we have available space to put the coin symmetrically opposite because each time before devil's move, the configuration is always symmetrical.

If we didn't put the coin at the center on the first move this wouldn't work because for any coin devil puts that overlaps with the center of the table we can't put the symmetrically opposite coin.

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wakiza33
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 Re: FAUSTIAN ROUND TABLE COIN GAME   « Reply #39 on: Sep 16th, 2014, 8:54am » Quote Modify

Put the quarters in the shape of a cross.
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