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ParthKohli Group Title

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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  1. ParthKohli Group Title
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    \[f(x,y)=f(y,x) \Rightarrow y^2x = x^2 y \]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
  2. ParthKohli Group Title
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    Are there any other ordered pairs where \(x \ne y\)?

    • one year ago
  3. ParthKohli Group Title
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    ZOMG, wait.

    • one year ago
  4. ParthKohli Group Title
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    \((-4)^2 \times -4 = (-4)^2 \times -4\)

    • one year ago
  5. ParthKohli Group Title
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    Facepalm. They can be negative.

    • one year ago
  6. electrokid Group Title
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    PING and the light turns on!

    • one year ago
  7. electrokid Group Title
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    :D

    • one year ago
  8. ParthKohli Group Title
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    lol yeah. That fetches me \(17 + 16 = 33\)

    • one year ago
  9. ParthKohli Group Title
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    Is 33 correct?

    • one year ago
  10. electrokid Group Title
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    no

    • one year ago
  11. ParthKohli Group Title
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    Aww.

    • one year ago
  12. electrokid Group Title
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    you have 33+16+16=?

    • one year ago
  13. ParthKohli Group Title
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    Why is that so?

    • one year ago
  14. electrokid Group Title
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    that many ordered pairs (0,?) and (?,0)

    • one year ago
  15. ParthKohli Group Title
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    Oh, I'm stupid. Thanks man!

    • one year ago
  16. electrokid Group Title
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    so, it'd be 33+32+32 ordered pairs

    • one year ago
  17. electrokid Group Title
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    how many ways can you have 1) x=0 2) y=0 3) x=y

    • one year ago
  18. ParthKohli Group Title
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    (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
  19. oldrin.bataku Group Title
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    Is this from brilliant.org?

    • one year ago
  20. ParthKohli Group Title
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    @oldrin.bataku Yeah, practicing stuff :-)

    • one year ago
  21. electrokid Group Title
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    this way you counted (0,0) twice

    • one year ago
  22. ParthKohli Group Title
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    Am I not allowed to ask questions for practice?

    • one year ago
  23. ParthKohli Group Title
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    @electrokid I subtracted it in the end.

    • one year ago
  24. electrokid Group Title
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    right.

    • one year ago
  25. oldrin.bataku Group Title
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    I'm not sure if you're allowed to ask for help on brilliant.org questions, at least publicly... :-p

    • one year ago
  26. perl Group Title
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    yes you are allowed

    • one year ago
  27. perl Group Title
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    and i am god

    • one year ago
  28. ParthKohli Group Title
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    @oldrin.bataku But I think I'm just practicing techniques.

    • one year ago
  29. perl Group Title
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    brilliant! 97 is the correct answer

    • one year ago
  30. electrokid Group Title
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    o'course it'd be lol

    • one year ago
  31. perl Group Title
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    u wbhi dheu dhee hee:)

    • one year ago
  32. electrokid Group Title
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    @perl what?

    • one year ago
  33. ParthKohli Group Title
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    @perl ?

    • one year ago
  34. perl Group Title
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    i said, i enjoyed the problem

    • one year ago
  35. perl Group Title
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    now i must go , there are babies to punish

    • one year ago
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