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anonymous
 5 years ago
find the total number of rectangles in a 8x9 chequered board.
anonymous
 5 years ago
find the total number of rectangles in a 8x9 chequered board.

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amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0or do you mean all permutations?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0its 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.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0i figured it wasnt that easy after i posted :) yeah, this is one of those...count the bigger versions of it... type issue

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0It'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

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0its aolt of counting :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0didnt really help.. :/

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.09C2 x 10C2 isn't a lot of counting.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0It's a lot of counting if you apply a medieval method, sure.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0anyway. i have another question

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0find 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?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I think we can assume you are wrong, yes; you can post an outline of your method for assessment, if you want.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i can explain how i derive mine. by doing the board from 1x1, 2x2,3x3, 4x4, it produces the answer

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.02x2> 4 3x3> 16 4x4> 36

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Firstly, a square is a type of rectangle.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0which follows a pattern of \[(2n2)^{2}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0my question stats that: think of the best way of specifying a rectangle. therefore i can decide whether to include squares as rectangles.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0for my benefit in this case i chose not to.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So it's actually: 1x1 > 1 2x2 > 9 (yours, plus the whole thing for 1, plus the 4 1x1s) 3x3 > 37 The pattern is actually \[1^3 + 2^3 + 3^3 + ... + ... n^3 \]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Firstly, you cannot decide a square isn't a rectangle. And second, your answer is still wrong.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0why is a square a rectangle?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0all squares are rectangles; but not all rectangles are squares.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0rectangle = opposites sides are the same; and 4, 90 degree corners

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0There 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.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Just a note  there was a typo above > 3x3 gives 36 not 37.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0actually a rectangle is a shape that has 2 equal sides.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0which makes square also a rectangle. ok i had that clarified thanks.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Actually, 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.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0a parallelogram is also a rectangle

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0No, 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.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok i'm sorry. i googled that and it told me that a parallelogram is a rectangular. guess it came out wrong.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0LOL. and newton who are you anyway? ^^

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0IF IT IS 3^3 THEN ANSWER IS 27 NOT 36???

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.03x3, 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.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0at leat no mistakes that anyone has lived to tell about ;)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0LOL. are you a lecturer? >.>

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0YOU R SAYING IT IS NOT A MISTAKE? FUNNY

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0how do you remove see out of this conversation?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0btw newton. can you help me in 8x9 rectangles?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ANY THING WRONG HOLYX?????????????

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0No, 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: \[^10C_2 \times ^9C_2 \text{ where } ^nC_r = \frac{n!}{r!(nr)!} \] You can do it by slower method of adding up systematically, but I will not partake in them.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ugh, LaTeX fail: \[^{10}C_2 \]**

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0wait im thinking. lol

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i dont get it. why 10c2. x 9c2. why do you need to multiply.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Because 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

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ugh, I mixed up vertical and horizontal in each part, but hopefully it made sense.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok yea. 9c2 x 9c2 gives the same aswer 1296!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0omg. you're damn smart. how did you thought of that. , wtf.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0anyway thanks for answering my question (:
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