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Topic: FRACTIONS THAT ADD TO 7 (Read 162 times) |
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pcbouhid
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FRACTIONS THAT ADD TO 7
« on: Nov 27th, 2005, 5:40am » |
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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.
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| « Last Edit: Nov 27th, 2005, 5:46am by pcbouhid » |
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Icarus
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Re: FRACTIONS THAT ADD TO 7
« Reply #1 on: Nov 27th, 2005, 9:25am » |
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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.
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pcbouhid
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Re: FRACTIONS THAT ADD TO 7
« Reply #2 on: Nov 27th, 2005, 12:54pm » |
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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.
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| « Last Edit: Nov 27th, 2005, 1:02pm by pcbouhid » |
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