[net.puzzle] A different balls-in-bowl puzzle

ark@rabbit.UUCP (Andrew Koenig) (02/15/84)

You have a bowl in front of you with a number of black and
white marbles in it.  You now repeat the following step:

	Remove two marbles from the bowl.  If they are the same
	color, put a white marble back.  If they are different colors,
	put a black marble back.

You have a sufficient supply of extra white marbles to accomplish this.
Since each step removes two marbles and replaces one, you will eventually
wind up with only a single marble in the bowl.  What color is it?
The answer is a function of the number of marbles of each color
that were originally in the bowl.

dcs@houxa.UUCP (D.SIMEN) (02/15/84)

> You have a bowl in front of you with a number of black and
> white marbles in it.  You now repeat the following step:
>
>	Remove two marbles from the bowl.  If they are the same
>	color, put a white marble back.  If they are different colors,
>	put a black marble back.
>
> You have a sufficient supply of extra white marbles to accomplish this.
> Since each step removes two marbles and replaces one, you will eventually
> wind up with only a single marble in the bowl.  What color is it?
> The answer is a function of the number of marbles of each color
> that were originally in the bowl.

In fact, the answer is a function only of the number of black marbles.

If you remove 2 black marbles (and add a white), the number of black
marbles has gone down by 2.  If you remove 2 whites (and replace 1) or
remove 1 of each color (and replace the black), the number of black
marbles stays the same.  In either case, the parity of the number of
black marbles is constant.  Therefore, if you start off with an even
number of black marbles, then when only 1 marble is left, it must be
white; if you start off with an odd number of blacks, you will end
up with 1 black and no white marbles.
						David Simen
						...!houxa!dcs

dcs@houxa.UUCP (D.SIMEN) (02/16/84)

Mea culpa (or "al het shehatati l'faneka" for the multilingual) --
I forgot to say "spoiler" in the title or first line of my solution
to this puzzle.  Won't do it again, if that's any consolation.

					David Simen
					...!houxa!dcs