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Black and White (Posted on 2003-02-25) Difficulty: 2 of 5
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
SolutionPuzzle SolutionK Sengupta2021-12-31 23:28:26
SolutionanswerStephen Ticsay2005-10-29 13:52:41
answergabbo2004-09-15 22:46:12
Balls!Denis Cronin2003-09-21 20:32:49
SolutionNo SubjectCaitlin2003-07-29 16:55:13
SolutionSolutionLewis2003-06-21 08:23:18
Solutionre: I believe it to be...Nich2003-06-10 08:06:40
umm my guess againJon2003-04-11 05:57:33
re(3): what do you mean not the answer?Ravi Raja2003-03-01 22:00:30
re(2): what do you mean not the answer?Lucifer2003-03-01 09:13:50
re: what do you mean not the answer?Ravi Raja2003-02-28 19:14:15
re:Ravi Raja2003-02-28 19:11:13
re: hiRavi Raja2003-02-28 19:08:57
re: i believe, does anyone?Ravi Raja2003-02-28 19:06:08
No SubjectLucifer2003-02-28 12:33:05
Questionwhat do you mean not the answer?Lucifer2003-02-28 12:30:50
hiGale2003-02-28 10:56:25
i believe, does anyone?fad2003-02-28 01:48:08
re: up a treeRavi Raja2003-02-27 20:25:34
re: I believe it to be...Ravi Raja2003-02-27 20:17:43
Questionre: up a treeLucifer2003-02-27 13:35:30
SolutionI believe it to be...Lucifer2003-02-27 13:32:58
up a treeSeth Sauer2003-02-26 05:59:13
re: ballroom dancingE Woodford2003-02-25 05:22:42
ballroom dancingNick Murray2003-02-25 02:07:09
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