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Nir Dahan Inner circle Munich, Germany 1390 Posts |
You got 15 coins.
one is good and marked so you could identify it among the rest. one of the other 14 is counterfeit and thus either heavier or lighter than the rest. with 3 scales weighting (comparative weighting) find the bad guy. Nir p.s. if you remember the old 12 coin puzzle this one will be quite easy |
stanalger Special user St. Louis, MO 998 Posts |
Has anyone cracked this one yet?
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stanalger Special user St. Louis, MO 998 Posts |
Nir,
Are we only required to indentify the counterfeit coin? Or are we also required to determine whether the counterfeit is heavy or light? |
Nir Dahan Inner circle Munich, Germany 1390 Posts |
Just identify - I didn't make it clear sorry
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stanalger Special user St. Louis, MO 998 Posts |
In that case, I've found a solution.
Will PM. |
stanalger Special user St. Louis, MO 998 Posts |
If I had been thinking clearly, I wouldn't have had to ask my
earlier question. Three weighings, three possible outcomes for each weighing (left pan heavy, right pan heavy, pans balance) means (even with a branching solution) 3^3 possible outcomes from the entire procedure. "Find counterfeit AND identify as heavy/light" would require one to distinguish between 2*14 = 28 different situations. Not possible with only 27 possible results of weighings. Stan |
stanalger Special user St. Louis, MO 998 Posts |
I don't want my last post to confuse anyone.
I was only pointing out that I didn't really need to ask Nir if we had to identify the counterfeit coin AND determine whether it was heavy or light. I had a "Duh!" experience and realized: THAT puzzle would be impossible. But Nir's instructions were clear enough: find the bad guy. (Don't worry about whether the bad guy is heavy or light.) Nir's puzzle DOES have a solution. In fact, you can find a non-branching solution. (A branching solution would be one in which the results of one weighing determine what coins go where in the next weighing.) |
Nir Dahan Inner circle Munich, Germany 1390 Posts |
Stan,
since no one has solved the puzzle maybe you should post your solution... |
stanalger Special user St. Louis, MO 998 Posts |
Here's one set of weighings that works.
Label each of the 14 suspect coins with a different letter from the phrase WARMLY COVETING and label the one coin known to be good ("Honest") with the letter H. Now weigh LYGHT against CRAVE HEAVY against CROWN WEIGH against ROYAL (If these weighings bring about an urge to imbibe a certain brand of Canadian Whiskey, I've done my job as a subliminal ad-man successfully.) If all comparison weighings result in "balance," M is the counterfeit. In this case, you don't know if M is light (lyght?) or heavy. For any other combination of results, you will easily be able to figure out which coin is counterfeit AND whether it is light or heavy. ****************************************************************************** If the misspelled "light" disturbs you too much, here's an alternative set of weighings: Label the 14 suspect coins with the letters of the phrase HYPNOTIC WAGERS and label the one coin known to be Legitimate with the letter L. Weigh WEIGH against PLOYS PITHY against SCALE HEAPS against CLOWN If all weighings result in balance, R is the counterfeit. Otherwise the results will enable you to not only determine which coin is counterfeit..but also whether the counterfeit is lighter or heavier than the legitimate coins. |
elmago Loyal user Northridge- Los Angeles, CA 272 Posts |
For me the problem is not understanding the question. Did you mean you only get 3 oppertunities to comparativley weigh the coins, then find a solution based on that?
The way I am reading it, I would take the coin I know is good and put it on one side of the scale. Then I would line up the other coins and compare the weight differance one by one. The first coin to show a differance in weight is the bad guy, AND, you would be able to tell if it is heavier or lighter. Hey, I might get lucky and get it within 3 tries. El Mago
"Excellence is not a single act; it's a habit" Shaq quoting Aristotle after winning NBA MVP.
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Nir Dahan Inner circle Munich, Germany 1390 Posts |
El mago,
you HAVE to do it in 3 tries and find a strategy that will give you a 100% chance to do so... otherwise what is the point... |
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