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: 7,635 Thanks: 2620 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: 14,299 Thanks: 1023 
Hint: 1,2,4,8,......

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 
Math Team Joined: Jul 2011 From: Texas Posts: 2,883 Thanks: 1503  
June 9th, 2017, 12:39 PM  #7 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,299 Thanks: 1023 
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  
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Quote:
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: 7,635 Thanks: 2620 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 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  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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