April 9th, 2017, 08:31 PM  #1 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 320 Thanks: 26 Math Focus: Number theory  Unique digital fractions sum to one
What equation ab/cd+efg/hij=1 is unique since it expresses "1" as sum of two fractions using all the digits from 0 to 9 exactly once each. Hint: both addends equal 1/2. 
April 9th, 2017, 09:55 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 1,790 Thanks: 923 
there seem to be quite a lot of solutions to this (over 14,000 before I stopped it)

April 9th, 2017, 10:19 PM  #3 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 320 Thanks: 26 Math Focus: Number theory 
Thanks to you, romsek, I now believe there is a considerable plurality of permutations  but over 14,000? I found the brainteaser online. 
April 9th, 2017, 10:27 PM  #4  
Senior Member Joined: Sep 2015 From: USA Posts: 1,790 Thanks: 923  Quote:
Didn't even need that long. There are 15264 numbers that satisfy this. Incidentally in all of them either the first or second term is 1. (and the other 0) Last edited by romsek; April 9th, 2017 at 10:41 PM.  
April 9th, 2017, 10:34 PM  #5 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 320 Thanks: 26 Math Focus: Number theory 
I'll sleep on it 
April 10th, 2017, 01:53 AM  #6 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 320 Thanks: 26 Math Focus: Number theory 
My question required that each term equal 1/2.

April 10th, 2017, 03:20 AM  #7 
Global Moderator Joined: Dec 2006 Posts: 18,719 Thanks: 1536 
For the equation's intended interpretation, 35/70 + 148/296 = 1.

April 10th, 2017, 08:52 AM  #8 
Senior Member Joined: Sep 2015 From: USA Posts: 1,790 Thanks: 923  
April 10th, 2017, 12:47 PM  #9 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 320 Thanks: 26 Math Focus: Number theory 
Let me ask that the 'hint' I gave rather be a 'requirement' of a problem: "Each addend must equal 1/2." __________ I have found that in mathematics, writing the problem is often over half of solving it. I am sorry if I wasted your time. 
April 10th, 2017, 12:49 PM  #10 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 320 Thanks: 26 Math Focus: Number theory 
skipjack found the correct solution given by my source.


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