The puzzle my bro asked me on the bus

[LuptonM]

You die and the devil says he'll let you go to heaven if you beat him in a game. The devil sits you down at a perfectly round table. He gives himself and you an infinite pile of quarters. He says, "OK, we'll take turns putting one quarter down, no overlapping allowed, and the quarters must rest flat on the table surface. The first guy who can't put a quarter down loses." You guys are about to start playing, and the devil says that he'll go first. However, at this point you immediately interject, and ask if you can go first instead. You make this interjection because you are very smart and can place quarters perfectly, and you know that if you go first, you can guarantee victory. Explain how you can guarantee victory, noting where u put the first coin


PS: good to know the devil is so civilised

 

[Steve Maskery]

I've disguised my solution in case anyone is still pondering. Wipe your mouse over to highlight and reveal.

1 Put the coin in the centre.
2 All the other coins go around in concentric circles. Each circle will have an even number of coins in it .

So as the Devil puts down the first coin in the first proper ring, you will always put the last.
S

 

[cambournepete]

I've disguised my solution in case anyone is still pondering. Wipe your mouse over to highlight and reveal.
<snip>
So as the Devil puts down the first coin in the first proper ring, you will always put the last.
S

I think you mean even rather than equal...

 

[LuptonM]

Its not really about concentric circles ( though u r pretty much right steve, although u simplified it a little) as u and the devil can place the coins anywhere (unless the devils OCD and likes everything neat). If u consider the diameter (ie. a line through the centre- the circle can be described by many diameters) and if you place the first coin in the centre, u must reflect whatever the devil does through the centre (the centre acts as a centre of inversion). If the devil can place a coin u can, since u r placing the coin in the reflection and thus u always place the last possible coin. If u note the total number of coins placed will be odd (if u use the symmetry strategy above), so u'll need to place the first one

NOTE hidden text be here

 

[Steve Maskery]

Pete, yes, thank you. Edited.

 

[Chems]

Too much like Uni work this.

If you enjoy this sort of stuff I can post up a few of the questions they ask us. Some are quite entertaining!

 

[PeterBassett]

Its not really about concentric circles ( though u r pretty much right steve, although u simplified it a little) as u and the devil can place the coins anywhere (unless the devils OCD and likes everything neat). If u consider the diameter (ie. a line through the centre- the circle can be described by many diameters) and if you place the first coin in the centre, u must reflect whatever the devil does through the centre (the centre acts as a centre of inversion). If the devil can place a coin u can, since u r placing the coin in the reflection and thus u always place the last possible coin. If u note the total number of coins placed will be odd (if u use the symmetry strategy above), so u'll need to place the first one

NOTE hidden text be here

i like that one. Very clever.

 

[Jacob]

Its not really about concentric circles ( though u r pretty much right steve, although u simplified it a little) as u and the devil can place the coins anywhere (unless the devils OCD and likes everything neat). If u consider the diameter (ie. a line through the centre- the circle can be described by many diameters) and if you place the first coin in the centre, u must reflect whatever the devil does through the centre (the centre acts as a centre of inversion). If the devil can place a coin u can, since u r placing the coin in the reflection and thus u always place the last possible coin. If u note the total number of coins placed will be odd (if u use the symmetry strategy above), so u'll need to place the first one

NOTE hidden text be here

Except it is nonsense isn't it? You can draw a circle so that only 1, 2, 3, 4 coins will fit, presumably ad infinitum.

 

[Steve Maskery]

How do you mean, Jacob?
All the coins are the same size and a table is many time bigger than any coin. So any pattern where all coins are touching at least two others is going to be hexagonal in structure and, therefore, essentially circular. Each circle has an even number, except the very centre (single coin), so it's always up to the Devil to start a new circle. It doesn't matter if the others are incomplete, they will have to be filled eventually. There will come a point when he can't continue.

S

 

[disco_monkey79]

Surely it's not up to the Devil as to who gets in to Heaven? Reckon he's trying to pull your leg. And I doubt St Pete would approve of the gambling...*




*I may have missed the point ;-)

 

[Carlow52]

Table is diameter of 1 coin :ho2

 

[Steve Maskery]

Table is diameter of 1 coin :ho2

In which case I win.

 

[Jacob]

How do you mean, Jacob?
All the coins are the same size and a table is many time bigger than any coin. So any pattern where all coins are touching at least two others is going to be hexagonal in structure and, therefore, essentially circular. Each circle has an even number, except the very centre (single coin), so it's always up to the Devil to start a new circle. It doesn't matter if the others are incomplete, they will have to be filled eventually. There will come a point when he can't continue.

S

No one said that they would all be touching at least two others! It still doesn't work however as the resultant regular polygon (approaching a circle in shape) could be offset assymetrically resulting in an incomplete outer circle of coins. e.g. if the nearest to the centre coin was 1/4 of it's diameter off the centre.
PS OK right - I just read the OP - if you can guarantee to hit the dead centre with first coin then you are the winner. Always read the small print! Anyway he didn't say anything about them touching at two points (or sliding them about)!

 

[Steve Maskery]

I'm very glad the Devil is fictitious, Jacob, I wouldn't want to inflict you on him. Or vice versa, come to that. I can just hear Andy Hamilton now...
"I though that Steve Maskery was a$%^&*() pedant but that Jacob takes the biscuit".

Meant in jocularity.
S

 

[Cowboy _Builder]

You put a coin right in the center of the table,after that, wherever the devil places his coin on the table, you mimic his placement on the opposite side of the table.
If he has a space to place a coin , so will you, and he will run out of places to put a coin before you do.