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FoolForMath
Group Title
Fool's problem of the day,
How many ordered pair of \((x,y)\) are there such that \(x, y \in \mathbb{Z} \) and \( \frac 2 x  \frac 3 y = \frac 1 4 \)
Good luck!
 2 years ago
 2 years ago
FoolForMath Group Title
Fool's problem of the day, How many ordered pair of \((x,y)\) are there such that \(x, y \in \mathbb{Z} \) and \( \frac 2 x  \frac 3 y = \frac 1 4 \) Good luck!
 2 years ago
 2 years ago

This Question is Closed

ParthKohli Group TitleBest ResponseYou've already chosen the best response.0
Oops, maybe this involves some trial and error :P
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.0
What is \(\mathbb{Z}\) in here?
 2 years ago

FoolForMath Group TitleBest ResponseYou've already chosen the best response.0
http://en.wikipedia.org/wiki/Integer
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.0
This works with 8 and 6
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.0
If b is 8 then a will be 16
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.0
I see a lot of solutions to this :/
 2 years ago

FoolForMath Group TitleBest ResponseYou've already chosen the best response.0
Not many, less than 25 I believe ;)
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.0
24 or 23 or 22.. I guess
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.0
The minimum of b is I guess 36 maximum is 84
 2 years ago

FoolForMath Group TitleBest ResponseYou've already chosen the best response.0
Don't guess, try to form a analytic approach :)
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.0
Oh wait, it goes further.
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.0
Your problem is hard.
 2 years ago

FoolForMath Group TitleBest ResponseYou've already chosen the best response.0
No spoiler please :)
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.0
How do we do it by the way?
 2 years ago

FoolForMath Group TitleBest ResponseYou've already chosen the best response.0
It's problem of the day, it's supposed to be interesting. However my approach takes less than 10 seconds ;) I will post it later though.
 2 years ago

Arnab09 Group TitleBest ResponseYou've already chosen the best response.1
is the answer 5? @FoolForMath ?
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.0
No Arnab.
 2 years ago

Arnab09 Group TitleBest ResponseYou've already chosen the best response.1
okay, we can get after simplification.. x=8y/(y+12) as x is an integer, 8y must be a multiple of y+12 8y=2*2*2*y so, here are possible equations y+12=1 y+12=2 y+12=4 y+12=8 y+12=2y y+12=4y y+12=8y as y +12 is a factor of 8y all the equations except the last one will satisfy for an integral value of y so, the answer is.. 6 ordered pairs
 2 years ago

Arnab09 Group TitleBest ResponseYou've already chosen the best response.1
sorry, there will be other options too if RHS is negative y+12=1 y+12=2 ................. and so on.. for y to be an integer, there are another 5 solutions so, total 11
 2 years ago

rfig.khalil Group TitleBest ResponseYou've already chosen the best response.0
is it right?
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.0
No, not right
 2 years ago

rfig.khalil Group TitleBest ResponseYou've already chosen the best response.0
the equation is equivalent to (x8)*(y+12)=96 so the answer is 11
 2 years ago

rfig.khalil Group TitleBest ResponseYou've already chosen the best response.0
is all the way wrong or just the 11?
 2 years ago

rfig.khalil Group TitleBest ResponseYou've already chosen the best response.0
I m pretty sur it's 22
 2 years ago

rfig.khalil Group TitleBest ResponseYou've already chosen the best response.0
is 24 correct answer.?
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.0
No, you are close by the way
 2 years ago

joemath314159 Group TitleBest ResponseYou've already chosen the best response.3
I was able to find 11 ordered pairs that are solutions: (7, 84) (6,36) (5,20) (4,12) (2,4) (4,4) (8,6) (16,8) (24,9) (40,10) (88,11) I think there might be more, but im missing an idea.
 2 years ago

FoolForMath Group TitleBest ResponseYou've already chosen the best response.0
HINT: There are 23 of them.
 2 years ago

FoolForMath Group TitleBest ResponseYou've already chosen the best response.0
Real challenge is to find a quick analytic approach :)
 2 years ago

joemath314159 Group TitleBest ResponseYou've already chosen the best response.3
yeah i just found the other 12, making 23.
 2 years ago

joemath314159 Group TitleBest ResponseYou've already chosen the best response.3
Most people probably got that:\[8y12xxy = 0\]There is a way you can factor this to get an idea of how many solutions there are...
 2 years ago

FoolForMath Group TitleBest ResponseYou've already chosen the best response.0
That's right joe! Congrats man!
 2 years ago

joemath314159 Group TitleBest ResponseYou've already chosen the best response.3
ty :)
 2 years ago
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