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 June 9th, 2017, 10:40 AM #1 Newbie   Joined: Jun 2017 From: Denmark Posts: 3 Thanks: 0 Almost impossible math question Hey guys. I'm in trouble. The question says: Ten tax collectors go to the king with 1000 gold coins each. Each gold coin weighs 10grams. Two tax collectors have "planed" 1gram of gold of each gold coin in their sack. Find with only ONE weighing the two cheating tax collectors. Impossible? Last edited by skipjack; June 9th, 2017 at 09:29 PM.
 June 9th, 2017, 11:01 AM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,675 Thanks: 2655 Math Focus: Mainly analysis and algebra Consider weighing different quantities of coins from each collector. Bear in mind that the scales are not balances. You'll get a number back as the weight of the coins you test.
 June 9th, 2017, 11:03 AM #3 Newbie   Joined: Jun 2017 From: Denmark Posts: 3 Thanks: 0 I've tried following: 1 coin from collector 1 2 coins from collector 2 etc. That's doesn't give me the answer. I'm kinda lost here
 June 9th, 2017, 12:21 PM #4 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 Hint: 1,2,4,8,...... Thanks from Djack
 June 9th, 2017, 12:32 PM #5 Newbie   Joined: Jun 2017 From: Denmark Posts: 3 Thanks: 0 How do I delete this post now?
June 9th, 2017, 12:35 PM   #6
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Quote:
 Originally Posted by Djack How do I delete this post now?
you can't ... it is now the intellectual property of this site.

 June 9th, 2017, 12:39 PM #7 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 PLUS we suggest you show how you got the solution: it may help another student. I'm SURE you're also interested in helping...
June 11th, 2017, 07:34 AM   #8
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Quote:
 Originally Posted by v8archie Consider weighing different quantities of coins from each collector. Bear in mind that the scales are not balances. You'll get a number back as the weight of the coins you test.
I'm terribly sorry sir but there is nothing in the statement of the problem that specifies the type of apparatus to be used for the weighing.

The wording of the problem , i.e. 'tax collectors bringing tax money to a king , 10000 gold pieces to boot!' , suggests that this is a problem from a long time ago , a time in which analog and/or digital readouts were not available.

 June 11th, 2017, 07:46 AM #9 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,675 Thanks: 2655 Math Focus: Mainly analysis and algebra And yet you are happy to take as read that we know that each coin weighs 10g and that some have had exactly 1g shaved off. If that can be determined, so can a numeric value for the weight of any given set of coins.
June 11th, 2017, 07:54 AM   #10
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 Originally Posted by v8archie And yet you are happy to take as read that we know that each coin weighs 10g and that some have had exactly 1g shaved off. If that can be determined, so can a numeric value for the weight of any given set of coins.
Not so fast. The technology to determine the weight of a gold coin to within a gram has been available for at least 500 years.

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