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From: HenHanna <HenHanna@dev.null>
Newsgroups: rec.puzzles
Subject: Re: Three rational triples
Date: Thu, 19 Sep 2024 02:39:59 +0000
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On Wed, 18 Sep 2024 22:39:45 +0000, Keith F. Lynch wrote:

> Keith F. Lynch <kfl@KeithLynch.net> wrote:
>> I discovered that these three sets of three positive rationals have
>> an interesting property in common:
>
>> 9/2, 4/3, 7/6
>> 49/15, 25/21, 54/35
>> 49/2, 4/7, 27/14
>
>> If nobody figures it out, I will provide the answer in a week.
>
> Since it's been more than a week, and nobody has figured it out:
>
> Each of them has a sum that's equal to its product and is an integer.


              i think  one person said  exactly that.


       Is it easy to find them?



How about 2 numbers

           2+2 = 2*2

           1+x = 1*x  ------- No sol.

           3+x = 3*x  -------  easy to solve.

           A+x = A*x  -------  all  easy to solve.








>
> For instance 9/2 + 4/3 + 7/6 = 7 and 9/2 x 4/3 x 7/6 = 7.
>
> Here are some more triples with this same unusual property:
>
> 121/42, 637/66, 36/77
> 81/5, 50/9, 11/45
> 625/18, 81/50, 148/225
> 289/15, 950/51, 9/85
> 49/3, 207/7, 2/21
> 450/13, 169/15, 23/195
> 25/2, 252/5, 1/10
> 81/2, 292/9, 1/18
> 242/5, 325/11, 3/55
> 121/2, 92/11, 3/22
> 625/21, 4214/75, 81/1575
> 676/7, 49/26, 99/182
> 245/3, 198/7, 1/21
> 343/3, 81/7, 2/21
> 578/5, 175/17, 9/85
> 529/3, 126/23, 13/69
> 289/2, 756/17, 1/34
> 525/2, 52/5, 1/10