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Real Test Of Genius


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"The scholarship will be awarded," said the head to three candidates - Chuckles, Wombat & Breeze - "to the winner in this little competition. I am going to chalk a cross, which will be either a green or a red cross. I shall then ask each one who can see a green cross to hold his hand up; and take his hand down as soon as he can tell me what his own cross is. He must, of course, be able to explain how his answer is arrived at. Kindly close your eyes for 10 seconds."

He chalked a green cross on all three foreheads. "Go!"

All three hands shot up in air ; that of Chuckles was almost immediately lowered. "My cross is green , Sir" 

How did Chuckles know?

More at https://spirit-of-genius.blogspot.in/2017/07/mind-blowing-brain-teaser.html

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I'd have got it quicker than the solution given via that link.

While I had my eyes shut, I'd realise that, assuming the test is fair, then it must be symmetrical with respect to interchange of any two candidates.

So, my cross must be the same colour as either of the other candidates (and their crosses must also be the same colour as eachother).

To be a fair test, all 3 candidates must have the same colour cross.

So I only have to blurt out the colour of  the first cross I see in order to win.

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This is oversimplified hypothetical story in which the winner was my friend!

One day Chuckles came to my home; he is my friend. I am 'smart' enough to immediately ask him story behind that mind teaser. What he had thought at that time is in his own words here...

"If I had red cross on my forehead then there is no way Wombat & Breeze raised their hand looking at me. What Wombat (or Breeze) would have thought in that case

Wombat (or Breeze) must have thought that Breeze (or Wombat) must have raised hand after looking green cross on my forehead as Chuckles have red cross on forehead.

So both would have come to know what they have on their own forehead & would have taken hands down immediately. But they didn't.

Hence I concluded, I must have green cross on my forehead & hence I took my hand down & earned the scholarship."
 

23 hours ago, John Cuthber said:

I'd have got it quicker than the solution given via that link.

While I had my eyes shut, I'd realise that, assuming the test is fair, then it must be symmetrical with respect to interchange of any two candidates.

So, my cross must be the same colour as either of the other candidates (and their crosses must also be the same colour as eachother).

To be a fair test, all 3 candidates must have the same colour cross.

So I only have to blurt out the colour of  the first cross I see in order to win.

Okay, but the your solution is based on the big assumption that the test is fair. How would we/participants know that the professor is very honest to present a fair contest? The link redirects you to the original puzzle.

Edited by Spiri.Of.Genius
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  • 2 months later...

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