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anonymous

  • 5 years ago

find the total number of rectangles in a 8x9 chequered board.

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  1. amistre64
    • 5 years ago
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    my guess is 72

  2. amistre64
    • 5 years ago
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    or do you mean all permutations?

  3. anonymous
    • 5 years ago
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    It's not 72.

  4. anonymous
    • 5 years ago
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    its not 72. the number is much bigger. this question is under the topic counting/progression. In order to do this you need to find the sequence; i.e. what is no. of rectangles. 1x2, 2x3, 3,4 board.

  5. amistre64
    • 5 years ago
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    i figured it wasnt that easy after i posted :) yeah, this is one of those...count the bigger versions of it... type issue

  6. anonymous
    • 5 years ago
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    help please! ><

  7. anonymous
    • 5 years ago
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    It's a pretty common problem, and am not in the mood to work through it myself, but this gives a pretty good explanation: http://mathforum.org/library/drmath/view/56760.html

  8. amistre64
    • 5 years ago
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    its aolt of counting :)

  9. anonymous
    • 5 years ago
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    didnt really help.. :/

  10. anonymous
    • 5 years ago
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    9C2 x 10C2 isn't a lot of counting.

  11. anonymous
    • 5 years ago
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    It's a lot of counting if you apply a medieval method, sure.

  12. anonymous
    • 5 years ago
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    anyway. i have another question

  13. anonymous
    • 5 years ago
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    find the total number of rectangles in 8x8 board. the answer in the link you gave me is 1296. but i got 196 instead. am i wrong?

  14. anonymous
    • 5 years ago
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    I think we can assume you are wrong, yes; you can post an outline of your method for assessment, if you want.

  15. anonymous
    • 5 years ago
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    i can explain how i derive mine. by doing the board from 1x1, 2x2,3x3, 4x4, it produces the answer

  16. anonymous
    • 5 years ago
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    1x1 -> 0

  17. anonymous
    • 5 years ago
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    2x2-> 4 3x3-> 16 4x4-> 36

  18. anonymous
    • 5 years ago
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    Firstly, a square is a type of rectangle.

  19. anonymous
    • 5 years ago
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    which follows a pattern of \[(2n-2)^{2}\]

  20. anonymous
    • 5 years ago
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    my question stats that: think of the best way of specifying a rectangle. therefore i can decide whether to include squares as rectangles.

  21. anonymous
    • 5 years ago
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    states*

  22. anonymous
    • 5 years ago
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    for my benefit in this case i chose not to.

  23. anonymous
    • 5 years ago
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    So it's actually: 1x1 -> 1 2x2 -> 9 (yours, plus the whole thing for 1, plus the 4 1x1s) 3x3 -> 37 The pattern is actually \[1^3 + 2^3 + 3^3 + ... + ... n^3 \]

  24. anonymous
    • 5 years ago
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    Firstly, you cannot decide a square isn't a rectangle. And second, your answer is still wrong.

  25. anonymous
    • 5 years ago
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    why is a square a rectangle?

  26. amistre64
    • 5 years ago
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    all squares are rectangles; but not all rectangles are squares.

  27. amistre64
    • 5 years ago
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    rectangle = opposites sides are the same; and 4, 90 degree corners

  28. anonymous
    • 5 years ago
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    There are 1296 rectangles. There are 204 squares. There are 1092 rectangles that are not squares. --- A rectangle is just a 4 sided shape with 4 right angles.

  29. anonymous
    • 5 years ago
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    Just a note - there was a typo above -> 3x3 gives 36 not 37.

  30. anonymous
    • 5 years ago
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    actually a rectangle is a shape that has 2 equal sides.

  31. anonymous
    • 5 years ago
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    which makes square also a rectangle. ok i had that clarified thanks.

  32. anonymous
    • 5 years ago
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    Actually, you don't need to say it has two equal sides (and that is not explicit enough - see: parallelogram). I direct you to my definition.

  33. anonymous
    • 5 years ago
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    a parallelogram is also a rectangle

  34. anonymous
    • 5 years ago
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    No, a rectangle is a parallelogram. The converse is not true - i.e. a parallelogram is not always a rectangle. Why are you arguing with me? You obviously have no idea who I am. That, and I'm trying to help you.

  35. anonymous
    • 5 years ago
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    ok i'm sorry. i googled that and it told me that a parallelogram is a rectangular. guess it came out wrong.

  36. anonymous
    • 5 years ago
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    3*3=36. HOW?

  37. anonymous
    • 5 years ago
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    *facepalm*

  38. anonymous
    • 5 years ago
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    its 1^3 + 2^3 + 3^3

  39. anonymous
    • 5 years ago
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    LOL. and newton who are you anyway? ^^

  40. anonymous
    • 5 years ago
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    IF IT IS 3^3 THEN ANSWER IS 27 NOT 36???

  41. anonymous
    • 5 years ago
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    3x3, in this context, means the number of rectangles on a 3x3 board. And I'm the person who has never made a Mathematical mistake in their entire life.

  42. amistre64
    • 5 years ago
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    at leat no mistakes that anyone has lived to tell about ;)

  43. anonymous
    • 5 years ago
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    LOL. are you a lecturer? >.>

  44. anonymous
    • 5 years ago
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    YOU R SAYING IT IS NOT A MISTAKE? FUNNY

  45. anonymous
    • 5 years ago
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    how do you remove see out of this conversation?

  46. anonymous
    • 5 years ago
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    btw newton. can you help me in 8x9 rectangles?

  47. anonymous
    • 5 years ago
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    ANY THING WRONG HOLYX?????????????

  48. anonymous
    • 5 years ago
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    No, I'm not a lecturer (or anything similar). And the number of rectangles on an 8 by 8 board can be obtained thus: There are 10 lines in one direction, and 9 lines in the others. To make a rectangle you need to pick 2 of each, so this is: \[^10C_2 \times ^9C_2 \text{ where } ^nC_r = \frac{n!}{r!(n-r)!} \] You can do it by slower method of adding up systematically, but I will not partake in them.

  49. anonymous
    • 5 years ago
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    8 by 9*

  50. anonymous
    • 5 years ago
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    Ugh, LaTeX fail: \[^{10}C_2 \]**

  51. anonymous
    • 5 years ago
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    you mean 8!/(8-r)!r!

  52. anonymous
    • 5 years ago
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    wait im thinking. lol

  53. anonymous
    • 5 years ago
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    i dont get it. why 10c2. x 9c2. why do you need to multiply.

  54. anonymous
    • 5 years ago
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    Because there are x ways to choose the horizontal lines, and y ways to chose the vertical ones, and therefore x * y ways to combine these. Say you choose the first set of line horizontally. You can pick any of the sets vertically to go with this. so this would be y ways. You then move onto the next way to pick vertical lines, and can do each of these with the horizontal ones, so another y ways. . You finally get to the xth set of vertical lines, and another y. Total = x * y

  55. anonymous
    • 5 years ago
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    Ugh, I mixed up vertical and horizontal in each part, but hopefully it made sense.

  56. anonymous
    • 5 years ago
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    ok yea. 9c2 x 9c2 gives the same aswer 1296!

  57. anonymous
    • 5 years ago
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    :)

  58. anonymous
    • 5 years ago
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    omg. you're damn smart. how did you thought of that. -,- wtf.

  59. anonymous
    • 5 years ago
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    anyway thanks for answering my question (:

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