Saturday, October 02, 2004

Puzzle Competition

Three puzzle competitors are blindfolded. A white piece of paper is glued to each competitor's forehead and they are told that not all of the pieces of paper are black. The blindfolds are removed and the competitors are told that the prize will go to the first to deduce whether the paper on his forehead is black or white.
The three competitors are silent for a short time, then all three announce white at the same time. Why?

Answers in the comments please. Note that there are two possible answers to this one - one relatively easy and intuitive, one harder and more 'logical'.


Anonymous Anonymous said...

This comment has been removed by a blog administrator.

October 2, 2004 at 10:19 PM  
Anonymous Anonymous said...

Hmm? Not sure what happened there, I didn't remove your comment Danielo! - plep

October 3, 2004 at 1:46 AM  
Blogger tom said...

This is a sticky one. I started typing a solution, then found a hole in my logic.

The 3 paused briefly. That would indicate that none saw the one thing that would assure a correct answer. After that I'm stuck. Can't wait for someone to solve this.


October 3, 2004 at 2:06 PM  
Blogger Sean said...

Man, my girlfriend is smart:

The key is the "pause". If there were 2 blacks and one white, the white person would have said something right away. If there were one black and 2 whites, white #1 would know that white #2 is looking at a white and a black (and therefore is pausing), which means that white #1 would have figured out that he's a white. Because white #1 is still not saying anything though, no one must be seeing a black. Therefore all 3 must be wearing white.

I'm so out of my league it's not even funny.

October 4, 2004 at 8:04 AM  
Blogger steven said...

Sean, your girlfriend is right! And I agree, this -is- a sticky one.

This puzzle comes from Boris A. Kordemsky's 'The Moscow Puzzles', a book of logical and mathematical puzzles published in the USSR in 1956.

Kordemsky's second (more intuitive) solution is agreeably socialist: For it to be a truly fair competition, all three contestants should be set the same puzzle to solve. Therefore a contestant could reason that if he sees two white pieces of paper, so should his fellows.

October 4, 2004 at 10:58 AM  
Blogger steven said...

Next puzzle will be this coming weekend.

October 4, 2004 at 11:16 AM  

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