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Subject: "Coin puzzle"     Previous Topic | Next Topic
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DdrgL
Charter Member
Nov-30-00, 09:57 AM (EST)
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"Coin puzzle"
 
   Hi,

This puzzle seems to be very esy at first. But it turns out to be tough. Lets try!
You have 12 coins that look identical. But, 1 coin is bogus and is either lighter or heavier than the others (!) You have a balance scale that can see if its two sides are equal.
Find the bogus coin and whether it is lighter or heavier than the others in only 3 weighings.


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alexb
Charter Member
672 posts
Dec-01-00, 10:03 AM (EST)
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1. "RE: Coin puzzle"
In response to message #0
 
   Please search my site for either "12 coin" or "Odd ball". There are several solutions and a nice discussion to be found.


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jon wegener (Guest)
guest
Dec-02-00, 00:55 AM (EST)
 
2. "RE: Coin puzzle"
In response to message #0
 
   i finally got the solution for 12 coins after agonizing for a day, but I dont have much insight into this amazing fact that you need only 3 weighings other than the influence of two facts: (1) the information gained at some steps is usually trinary (+, =, -) not binary (yes, no) becasue the scale can remain unbalanced, become balaneced, or flip and (2) also if the removed coins have been determined to be normal they provide a reference state which again provides 3 pieces of info (normal, heavy, or light) when used to compare uncertain coins on the balance.

My question is this: I generalized this to n coins to see where the divide between 2 and 3 weighings occurs. It'seems solvable with 2 weighs only up to 4 coins (one bogus), but did I miss a way to solve it with only 2 weighings with say 5 or 6?? If 4 is correct, it is also amazing, because it means that 3 weighings works over a very large range, up to 12 at least!!


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alexb
Charter Member
672 posts
Dec-03-00, 01:06 AM (EST)
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3. "RE: Coin puzzle"
In response to message #2
 
   LAST EDITED ON Dec-03-00 AT 01:14 AM (EST)

Please read

https://cut-the-knot.com/blue/weight1.shtml

and follow the links at the bottom of the page


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