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Consider the function on the integers given by \(f(x,y)=x^2y\). How many ordered pairs of integers satisfying \(−16\le x,y\le16\) is \(f(x,y)=f(y,x)\)?
 one year ago
 one year ago
Why is my answer wrong? Consider the function on the integers given by \(f(x,y)=x^2y\). How many ordered pairs of integers satisfying \(−16\le x,y\le16\) is \(f(x,y)=f(y,x)\)?
 one year ago
 one year ago

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ParthKohliBest ResponseYou've already chosen the best response.2
\[f(x,y)=f(y,x) \Rightarrow y^2x = x^2 y \]I observed that \(x\) and \(y\) cannot be negative here. So I am left with numbers ranging from \(0\) to \(16\). That gives me \(17\).
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.2
Are there any other ordered pairs where \(x \ne y\)?
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.2
\((4)^2 \times 4 = (4)^2 \times 4\)
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.2
Facepalm. They can be negative.
 one year ago

electrokidBest ResponseYou've already chosen the best response.2
PING and the light turns on!
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.2
lol yeah. That fetches me \(17 + 16 = 33\)
 one year ago

electrokidBest ResponseYou've already chosen the best response.2
you have 33+16+16=?
 one year ago

electrokidBest ResponseYou've already chosen the best response.2
that many ordered pairs (0,?) and (?,0)
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.2
Oh, I'm stupid. Thanks man!
 one year ago

electrokidBest ResponseYou've already chosen the best response.2
so, it'd be 33+32+32 ordered pairs
 one year ago

electrokidBest ResponseYou've already chosen the best response.2
how many ways can you have 1) x=0 2) y=0 3) x=y
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.2
(1,1),(2,2)...(16,16) is 16. (1,1)...(16,16) is 16. (0,?) is 33. (?,0) is 33. 32 + 33 + 33 = 98 We overcounted a (0,0), so 32 + 32 + 33 = 97. Right?
 one year ago

oldrin.batakuBest ResponseYou've already chosen the best response.0
Is this from brilliant.org?
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.2
@oldrin.bataku Yeah, practicing stuff :)
 one year ago

electrokidBest ResponseYou've already chosen the best response.2
this way you counted (0,0) twice
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.2
Am I not allowed to ask questions for practice?
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.2
@electrokid I subtracted it in the end.
 one year ago

oldrin.batakuBest ResponseYou've already chosen the best response.0
I'm not sure if you're allowed to ask for help on brilliant.org questions, at least publicly... :p
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.2
@oldrin.bataku But I think I'm just practicing techniques.
 one year ago

perlBest ResponseYou've already chosen the best response.0
brilliant! 97 is the correct answer
 one year ago

electrokidBest ResponseYou've already chosen the best response.2
o'course it'd be lol
 one year ago

perlBest ResponseYou've already chosen the best response.0
i said, i enjoyed the problem
 one year ago

perlBest ResponseYou've already chosen the best response.0
now i must go , there are babies to punish
 one year ago
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