Another logic puzzle

Arcade Fire · 18 Oct 2006 at 10:43

I'm going to tell you about a game. The board for this game is a circular disc of an arbitrary size. All of the playing pieces are also circular discs, all the same size and all smaller than the board.

The two players take turns to place their pieces on the board. You can't place a piece on top of a piece that's already there. The first person who is unable to make a legal move loses.

You have the choice as to whether you're going first or second - which should you choose, and WHY?

Arcade Fire · 18 Oct 2006 at 10:48

That would be the correct answer if I'd said that the pieces were only a bit smaller than the board, but I didn't. The pieces can be of any size, as long as they're all the same size and they're smaller than the board.

Arcade Fire · 18 Oct 2006 at 10:55

kaiowas said:
When you place a piece does it have to be entirely on the board or do you need just enough on there for it to stay on under it's own weight?

Also are you allowed to move existing pieces when placing a piece?

Not that it matters, but for the sake of argument let's say that you have to place the pieces entirely on the board.

You can't move any pieces that have already been played.

Arcade Fire · 18 Oct 2006 at 10:57

addy_010 said:
does it matter though, i thought that if your on the board your on it taking up that one piece meaning there is no where for the second piece to be put down?

What?

Arcade Fire · 18 Oct 2006 at 10:59

If it was that simple I don't think I would have bothered making the thread. Since I evidently did bother making the thread, I think you are safe to deduce that it's not that simple.

Arcade Fire · 18 Oct 2006 at 11:01

SiriusB said:
Okay wild stab in the dark now... I reckon you wanna go first because of the way you lay down the circles.

Logically the first person will put a piece in the middle... then a ring of pieces would form around that, and then another ring around that and so on until no more space... now since the first person has the advantage of the very middle spot, I reckon first will win

I didn't say that the pieces have to be laid down next to other pieces.

Why will the first person always play in the middle?

Arcade Fire · 18 Oct 2006 at 11:14

badgermonkey said:
BEcause if you go first you know that you could win that way?

Your opponent isn't going to place pieces where you want him to, though, is he?

Arcade Fire · 18 Oct 2006 at 11:14

fatiain said:
Sounds like a *great* game.

Is that your way of saying "I'm not clever enough to work out the answer"?

Arcade Fire · 18 Oct 2006 at 11:36

Okay, I'll spot you a hint. The correct answer is that you should choose to go first, and that you should make your first move in the centre of the board. How should you play from there, to guarantee your win?

Arcade Fire · 18 Oct 2006 at 11:57

semi-pro waster said:
Then I'd guess place each one of your counters just inside the diameter of a counter in all directions, e.g. if the counter has a diameter of 5cm then you place it at 4.9cm and you will win due to some property of circles and area. I could potentially work it out but I've forgotten most of the maths that I ever knew And I still would probably do my idea first anyway just because I'm like that.

Nope.

Arcade Fire · 18 Oct 2006 at 12:19

Bill Door said:
I opt to play first and place my counter in the centre, then place any subsequent counters symetrically opposite to those played by my opponent.

If there is space remaining for my opponent to place a counter then logically there must be a space remaining for me to play.

Bingo.

Arcade Fire · 18 Oct 2006 at 12:31

Noughts and crosses is interesting (ish). If both players play perfectly then it's impossible to win, whether you go first or second. There are a couple of ways to win if you go first and your opponent doesn't make the optimal second move. If you play in one of the corners then your opponent has to play in the centre. If he doesn't then you can beat him.