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 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.

 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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