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.
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.
On 9/11/2024 5:15 AM, Keith F. Lynch 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.
that sounds good.
I discovered that these three sets of three positive rationals have an interesting property in common:
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.
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.
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
Keith F. Lynch wrote:
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
Keith F. Lynch wrote:
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.
On Fri, 13 Sep 2024 2:19:31 +0000, HenHanna wrote:
On 9/11/2024 5:15 AM, Keith F. Lynch 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.
that sounds good.
SPOILER
The sum of each triplet is the same as its product.
9/2*4/3*7/6 = 9/2+4/3+7/6 = 7
49/15*25/21*54/35 = 49/15+25/21+54/35 = 6
49/2*4/7*27/14 = 49/2+4/7+27/14 = 27
Please reply to ilanlmayer at gmail dot com
__/\__
\ /
__/\\ //\__ Ilan Mayer
\ /
/__ __\ Toronto, Canada
/__ __\
||
On 9/11/2024 5:15 AM, Keith F. Lynch 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.
that sounds good.
So this post below didn't get to your site (or Newsreader).
IlanMayer wrote:
. . .
The sum of each triplet is the same as its product.
9/2*4/3*7/6 = 9/2+4/3+7/6 = 7
49/15*25/21*54/35 = 49/15+25/21+54/35 = 6
49/2*4/7*27/14 = 49/2+4/7+27/14 = 27
Please reply to ilanlmayer at gmail dot com
__/\__
\ /
__/\\ //\__ Ilan Mayer
\ /
/__ __\ Toronto, Canada
/__ __\
||
HenHanna <HenHanna@dev.null> wrote:
Keith F. Lynch wrote:
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.
Who and when? I didn't see any such post.
Is it easy to find them?
No, even though there are infinitely many. Try and find one I
didn't list.
Constraints: All three numbers must be positive, real, and rational,
but not integers.
"Keith F. Lynch" <kfl@KeithLynch.net> writes:
HenHanna <HenHanna@dev.null> wrote:
Keith F. Lynch wrote:
Each of them has a sum that's equal to its product and is an integer.
They're literally everywhere. Given 2 rational numbers, there's a solution
(Here I've capped numerators and denominators to 50.)
I'm particularly enamoured with this find:
4/3 7/6 9/2 7=7
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