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 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
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 \(f(x,y)=f(y,x)\)?

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ParthKohli
 one year ago
Best 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 \(17\).

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

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

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

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

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

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

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

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

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

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

ParthKohli
 one year ago
Best 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?

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

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

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

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

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

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

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

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

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

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

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