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 April 9th, 2017, 08:31 PM #1 Senior Member   Joined: May 2015 From: Arlington, VA Posts: 374 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: 2,091 Thanks: 1087 there seem to be quite a lot of solutions to this (over 14,000 before I stopped it) Thanks from Loren
 April 9th, 2017, 10:19 PM #3 Senior Member   Joined: May 2015 From: Arlington, VA Posts: 374 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
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Quote:
 Originally Posted by Loren Thanks to you, romsek, I now believe there is a considerable plurality of permutations -- but over 14,000? I found the brainteaser online.
I can let it run overnight and see just how many there are

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: 374 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: 374 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: 19,508 Thanks: 1742 For the equation's intended interpretation, 35/70 + 148/296 = 1.
April 10th, 2017, 08:52 AM   #8
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Quote:
 Originally Posted by Loren My question required that each term equal 1/2.
you need to learn to write questions then.

Adding something as a "hint" doesn't make it a requirement of the problem.

 April 10th, 2017, 12:47 PM #9 Senior Member   Joined: May 2015 From: Arlington, VA Posts: 374 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: 374 Thanks: 26 Math Focus: Number theory skipjack found the correct solution given by my source.

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