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        riddles >> medium >> FRACTIONS THAT ADD TO 7
        
(Message started by: pcbouhid on Nov 27^th, 2005, 5:40am)

Title: FRACTIONS THAT ADD TO 7
Post by pcbouhid on Nov 27^th, 2005, 5:40am

Using the digits 1-->9 once each, one wrote two fractions that add to 7, as below:

AB FG
-------- + -------- = 7
CDE HI

Find the fractions.

Note: there is more than one solution.

Title: Re: FRACTIONS THAT ADD TO 7
Post by Icarus on Nov 27^th, 2005, 9:25am

I never cared much for these things, which mainly require trial-and-error solutions, but I will note that in any solution to this, H=1, I <= 6 and F >= 7.

For, Since C>0, AB < CDE and so AB/CDE < 1. Thus FG/HI > 6. Since 6*17 = 102, HI < 17. 12 is the smallest 2 digit number with distinct digits >0, So HI >= 12, which means FG > 6*12 = 72.

Title: Re: FRACTIONS THAT ADD TO 7
Post by pcbouhid on Nov 27^th, 2005, 12:54pm

My idea of this type of problem is the same as yours, but the search can be narrowed by some reasoning and a systematic trial and error, which means "sufficient available time". Or a computer!

In "my" problem "where are the digits?", the author says that for a long time, everybody thought that it could be solved only with a computer. In one of his books, he presents a solution (with reasoning) that fills almost 4 pages. But in nowadays it serves only for one to improve his techniques in computer progamming.