- 09 Sep '05 02:45You have a bag with 50 balls in it. 25 of the balls are white, and 25 are black. You draw two balls from the bag at a time. You don't know what color the balls are until you have removed them from the bag. If you draw two white balls, or two black balls, you place a white ball in the bag. If the draw is two balls of different color, you place a black ball in the bag. What is the color of the last ball in the bag? If you start with n white balls, and n black balls, when is the last ball white, and when is the last ball black?
- 09 Sep '05 18:14

Very good. You are quite a problem solver. If anyone is interested in Mephisto's logic, PM me, and I'll give you the answer.*Originally posted by Mephisto2***Just a guestimate: if n=even, you end with a white ball, if n= odd you end with a black ball, as in the case with 25 white and 25 black balls.** - 09 Sep '05 19:12

Just messing around with this...if you let the number of balls be different, say "n" black balls and "m" white balls, it turns out that the final colour depends only on the oddness/evenness (parity) of "n", the number of black balls. Interesting!*Originally posted by rheymans***Very good. You are quite a problem solver. If anyone is interested in Mephisto's logic, PM me, and I'll give you the answer.** - 10 Sep '05 00:30

Yes, that is right. The white balls are pretty much a distraction in this problem.*Originally posted by PBE6***Just messing around with this...if you let the number of balls be different, say "n" black balls and "m" white balls, it turns out that the final colour depends only on the oddness/evenness (parity) of "n", the number of black balls. Interesting!** - 13 Sep '05 00:48 / 1 edit

This problem might not be properly stated.*Originally posted by rheymans***You have a bag with 50 balls in it. 25 of the balls are white, and 25 are black. You draw two balls from the bag at a time. You don't know what color the balls are until you have removed them from the bag. If you draw two white balls, or two black balls, you place a white ball in the bag. If the draw is two balls of different color, you place a black ...[text shortened]... n white balls, and n black balls, when is the last ball white, and when is the last ball black?**

1) What if you draw one black and one white ball ?

2) Is there a separate bag ?

3) Are black and white really colors? - 13 Sep '05 02:50

1) What if you draw one black and one white ball ?*Originally posted by eldragonfly***This problem might not be properly stated.**

1) What if you draw one black and one white ball ?

2) Is there a separate bag ?

3) Are black and white really colors?

This is the case when the two balls are different colors.

2) Is there a separate bag ?

No.

3) Are black and white really colors?

Although it is not important, if it means so much to you, call them red, and green balls instead of black, and white. In any case, if you went to a paint store, and you asked for what colors they have available, I'm sure that black, and white would be mentioned. I would like to read a sentence that uses black, or white as an adjective, and said adjective does not imply the color of what it describes. - 13 Sep '05 03:25

Good point.*Originally posted by rheymans***Although it is not important, if it means so much to you, call them red, and green balls instead of black, and white. In any case, if you went to a paint store, and you asked for what colors they have available, I'm sure that black, and white would be mentioned. I would like to read a sentence that uses black, or white as an adjective, and said adjective does not imply the color of what it describes.**