
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
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September 28th, 2019, 02:54 AM  #1 
Newbie Joined: Sep 2019 From: ireland Posts: 3 Thanks: 0  proof
abc and bca are 3 digit numbers.show that abccba is divided by 11

September 28th, 2019, 04:51 AM  #2 
Senior Member Joined: Jun 2014 From: USA Posts: 620 Thanks: 52 
If I let a=b=c, I seem to be getting a funny result.

September 28th, 2019, 05:06 AM  #3 
Senior Member Joined: Jun 2014 From: USA Posts: 620 Thanks: 52 
321  213 = 108 where 108 is not divisible by 11.

September 28th, 2019, 09:42 AM  #4 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,690 Thanks: 2669 Math Focus: Mainly analysis and algebra 
But 321  123 = 198 which is divisble by 11. \begin{align} (100a + 10b + c)  (100c + 10b + a) &= 99a  99c \\ &= 11( 9a9c) \end{align} I have no idea what bca has to do with the price of fish. Last edited by v8archie; September 28th, 2019 at 09:46 AM. 
September 28th, 2019, 01:20 PM  #5 
Senior Member Joined: Mar 2015 From: Universe 2.71828i3.14159 Posts: 132 Thanks: 49 Math Focus: Area of Circle 
it is abccba
