ParthKohli 2 years 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 $$f(x,y)=f(y,x)$$?

1. ParthKohli

$f(x,y)=f(y,x) \Rightarrow y^2x = x^2 y$I observed that $$x$$ and $$y$$ cannot be negative here. So I am left with numbers ranging from $$0$$ to $$16$$. That gives me $$17$$.

2. ParthKohli

Are there any other ordered pairs where $$x \ne y$$?

3. ParthKohli

ZOMG, wait.

4. ParthKohli

$$(-4)^2 \times -4 = (-4)^2 \times -4$$

5. ParthKohli

Facepalm. They can be negative.

6. electrokid

PING and the light turns on!

7. electrokid

:D

8. ParthKohli

lol yeah. That fetches me $$17 + 16 = 33$$

9. ParthKohli

Is 33 correct?

10. electrokid

no

11. ParthKohli

Aww.

12. electrokid

you have 33+16+16=?

13. ParthKohli

Why is that so?

14. electrokid

that many ordered pairs (0,?) and (?,0)

15. ParthKohli

Oh, I'm stupid. Thanks man!

16. electrokid

so, it'd be 33+32+32 ordered pairs

17. electrokid

how many ways can you have 1) x=0 2) y=0 3) x=y

18. ParthKohli

(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?

19. oldrin.bataku

Is this from brilliant.org?

20. ParthKohli

@oldrin.bataku Yeah, practicing stuff :-)

21. electrokid

this way you counted (0,0) twice

22. ParthKohli

Am I not allowed to ask questions for practice?

23. ParthKohli

@electrokid I subtracted it in the end.

24. electrokid

right.

25. oldrin.bataku

I'm not sure if you're allowed to ask for help on brilliant.org questions, at least publicly... :-p

26. perl

yes you are allowed

27. perl

and i am god

28. ParthKohli

@oldrin.bataku But I think I'm just practicing techniques.

29. perl

brilliant! 97 is the correct answer

30. electrokid

o'course it'd be lol

31. perl

u wbhi dheu dhee hee:)

32. electrokid

@perl what?

33. ParthKohli

@perl ?

34. perl

i said, i enjoyed the problem

35. perl

now i must go , there are babies to punish