Est. 1998 — 27 years of woodworking knowledge
Tuesday - wooden nickels
Bill Earl
The game is played on a round table of any size. Both you and your opponent have a large bag of wooden nickels - all of the same size. Players take turns placing coins on the table until no more coins can be placed. The player that placed the last wooden nickel wins.
Coins must not overlap or hang over the edge of the table. Coins already on the table cannot be moved.
Your opponent offers you the chance to go first. Do you take it?
Re: Tuesday - wooden nickels
John Veerkamp
It may be odd but I'd always go first.
Re: Tuesday - wooden nickels
Alex Y
I'd have to recuse myself.
And your strategy?
Re: Tuesday - wooden nickels
Larry Barrett
If the table has a diameter = the diameter of the coin, clearly going first is the right strategy (tables with diameters less than the diameter of the coin must be excluded).
If the table has a diameter < 3 times the diameter of the coin, going first and placing you coin in the center is a winning move.
Beyond 3 times is not obvious, but if the strategy is independent of the table size, then going first would be what I would do.
There is a strategy
Bill Earl
There is a strategy that guarantees a win. It works for any table size (>= the size of the coin of course)
Hint
Bill Earl
Given the first move, there is a strategy that will guarantee a win.
The strategy will work on a table of any size.
It will also work on tables of different shapes - e.g. square, rectangular, oval, elliptical.
In fact, there are an infinite number of shapes on which it will work.
But there are also an infinite number of shapes on which it will not.
Re: Hint
Larry Barrett
How about first move in the center, then mirror your opponent's move. If he can make a move, you can too. If he can't, you win.
Bill Earl
That's it! This will work on a table of any size - and any shape that has 180 degree rotational symmetry.