perplexus.info :: Logic : Black and White

Black and White (Posted on 2003-02-25)

Imagine that you have three boxes, one containing two black balls, one containing two white balls, and the third containing one black ball and one white ball.

The boxes were originally labelled for their contents (BB - WW - BW) but someone has inadvertently switched the labels so that now every box is incorrectly labelled.

Without looking inside, you are allowed to take one ball at a time out of any box that you wish, and by this process of sampling, you are to determine the contents of all three boxes.

What is the smallest number of drawings needed to do this?

Submitted by Ravi Raja

Rating: 3.1250 (8 votes)

Solution: (Hide)

You need only take one ball to re-label the jars properly. The key is that all the labels are wrong. So, the jar labeled BW has either all black balls or all white balls. Take one ball from that jar, and figure out which one it is.
Now, if this is the black jar, then the jar labeled "black" is really the white jar, and the remaining one is mixed.
On the other hand, if the first jar is white, then the jar labelled "white" is actually black, the remaining being mixed once again.
As you see, there are only two possibilities, and you can figure out which one is actually true by removing the ball from the jar whose label says its mixed.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Solution	K Sengupta	2021-12-31 23:28:26
answer	Stephen Ticsay	2005-10-29 13:52:41
answer	gabbo	2004-09-15 22:46:12
Balls!	Denis Cronin	2003-09-21 20:32:49
No Subject	Caitlin	2003-07-29 16:55:13
Solution	Lewis	2003-06-21 08:23:18
re: I believe it to be...	Nich	2003-06-10 08:06:40
umm my guess again	Jon	2003-04-11 05:57:33
re(3): what do you mean not the answer?	Ravi Raja	2003-03-01 22:00:30
re(2): what do you mean not the answer?	Lucifer	2003-03-01 09:13:50
re: what do you mean not the answer?	Ravi Raja	2003-02-28 19:14:15
re:	Ravi Raja	2003-02-28 19:11:13
re: hi	Ravi Raja	2003-02-28 19:08:57
re: i believe, does anyone?	Ravi Raja	2003-02-28 19:06:08
No Subject	Lucifer	2003-02-28 12:33:05
what do you mean not the answer?	Lucifer	2003-02-28 12:30:50
hi	Gale	2003-02-28 10:56:25
i believe, does anyone?	fad	2003-02-28 01:48:08
re: up a tree	Ravi Raja	2003-02-27 20:25:34
re: I believe it to be...	Ravi Raja	2003-02-27 20:17:43
re: up a tree	Lucifer	2003-02-27 13:35:30
I believe it to be...	Lucifer	2003-02-27 13:32:58
up a tree	Seth Sauer	2003-02-26 05:59:13
re: ballroom dancing	E Woodford	2003-02-25 05:22:42
ballroom dancing	Nick Murray	2003-02-25 02:07:09

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