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18 crystals Weighing puzzles  Weight: 5 Liked the puzzle: 100% 30.12.2009
Once upon a time, a Megamind worked as an optometrist for an Occupier who was color blind. The Occupier had a dream that he may regain perfect vision if the Megamind made him a set of 9 red and 9 blue crystals. The crystals should be of the same size, but the blue ones should be heavier than the red ones. Crystals of the same color should weigh the same. The Megamind completed the order and brought two sets of crystals: blue in his right hand and red in the left. The Occupier was suspicious, he did not trust the Megamind. Fortunately, the Occupier has a balance scale. How can the Megamind convince the Occupier that all crystals in one hand are blue and in the other - red. He can use no more than three weighings.
Comments:   5 check your solution  

Please do not post comments containing clues, hints, or anything that might be considered as a hint to others. All such comments will be deleted. If you have a question, you can contact a moderator by clicking the button "Submit your solution".

idler_
 
Rating: 106
Group: Moderators
2011-01-28 19:40:27
Reserved.
dddfff
 
Rating: 228
Group: Moderators
2011-03-13 22:29:25
The story of the problem refers to "blue in his right hand and red in the left." But the challenge only asks that the Megamind "convince the Occupier that all crystals in one hand are blue and in the other - red."

That's one bit of information less than "convince the Occupier that all crystals in his right hand are blue and in his left - red."

Does a solution require the Megamind to establish that final bit?


dddfff
 
Rating: 228
Group: Moderators
2011-03-14 21:56:12
Another thing that isn't clear to me from the problem statement: do Megamind and Occupier agree that that Megamind has indeed brought 9 blue and 9 red crystals, so the question only concerns which hand has which crystals? Or does the possibility exist in the mind of the Occupier, that, say, all the crystals might be red?
alan
 
Rating: 231
Group: Moderators
2011-03-17 11:00:21
dddfff 2011-03-13 22:29:25
The story of the problem refers to "blue in his right hand and red in the left." But the challenge only asks that the Megamind "convince the Occupier that all crystals in one hand are blue and in the other - red."

That's one bit of information less than "convince the Occupier that all crystals in his right hand are blue and in his left - red."

Does a solution require the Megamind to establish that final bit?

Solution does not require this.
But, do you really think that it is possible to complete the task and do Not establish that final bit?

dddfff 2011-03-14 21:56:12
Another thing that isn't clear to me from the problem statement: do Megamind and Occupier agree that that Megamind has indeed brought 9 blue and 9 red crystals, so the question only concerns which hand has which crystals? Or does the possibility exist in the mind of the Occupier, that, say, all the crystals might be red?

No, they do not agree. And yes, such possibility exists.
Occupier know (believe) only that "blue ones is heavier than the red ones"
dddfff
 
Rating: 228
Group: Moderators
2011-03-19 10:37:40
>But, do you really think that it is possible to complete the task and do Not establish that final bit?

Sadly, lacking a solution, I am agnostic on this question, but it does mean that I can't rule out, a priori, strategies where the scale balances all three times. So in some sense this leniency actually makes the problem harder!



 
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