Countolaf
Level 11 poster
Count Omar, the Wild Warrior
Posts: 1,113
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Post by Countolaf on May 14, 2006 19:48:04 GMT 1
There is one counterfeit coin among 1000 similar coins. It is not known whether the counterfeit coin is lighter or heavier than a genuine coin. What is the least number of weighings, on a pan balance, necessary to locate the counterfeit and to determine whether it is lighter or heavier?
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scotchy
Level 0 poster
The Sorcerer knight
Posts: 48
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Post by scotchy on May 14, 2006 19:57:24 GMT 1
absolute min I got would be 6 times.
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Post by Fox Mc Cloud on May 14, 2006 20:57:31 GMT 1
I think 6 too.
333-111-37-12-4-1
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Countolaf
Level 11 poster
Count Omar, the Wild Warrior
Posts: 1,113
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Post by Countolaf on May 15, 2006 20:40:00 GMT 1
It is not 6. Hmm... read the question well  |
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Post by Fox Mc Cloud on May 15, 2006 22:00:14 GMT 1
1) 333 VS 333 so aside: 334
2) 111 VS 111 so aside: 111 or 112
3) 37 VS 37 so aside: 37 or 38
4) 12 VS 12 so aside: 13 or 14
5) 4 VS 4 so aside: 4 or 5 or 6
6) if 4: 2 VS 2 - if 5: 2 VS 2 and 1 aside - if 6: 2 VS 2 and 2 aside
7) 1 VS 1 and if in balance then it's the coin aisde
--> So 7
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scotchy
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The Sorcerer knight
Posts: 48
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Post by scotchy on May 15, 2006 22:18:44 GMT 1
its actually a trick question, the minimum could be 2... hehe
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Countolaf
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Count Omar, the Wild Warrior
Posts: 1,113
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Post by Countolaf on May 15, 2006 22:36:55 GMT 1
The answer is 7, but Fox's solution isn't correct Ah, Scotchy, least number of weighings is meaning minimum number of tries to be sure you will find the counterfeit coin and determine whether it is lighter or heavier, being the less lucky person in the world. |
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scotchy
Level 0 poster
The Sorcerer knight
Posts: 48
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Post by scotchy on May 16, 2006 1:47:08 GMT 1
I know, but I love technicalities xD
I know how its done by the way all it takes is one extra weighing in the beginning to see which piles match up.
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Post by Fox Mc Cloud on May 16, 2006 6:12:49 GMT 1
The answer is 7, but Fox's solution isn't correct Ah, Scotchy, least number of weighings is meaning minimum number of tries to be sure you will find the counterfeit coin and determine whether it is lighter or heavier, being the less lucky person in the world. My solution works, just give me 1000 coins and I'll show you.  |
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