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

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

Mathematics
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my guess is 72
or do you mean all permutations?
It's not 72.

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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.
i figured it wasnt that easy after i posted :) yeah, this is one of those...count the bigger versions of it... type issue
help please! ><
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
its aolt of counting :)
didnt really help.. :/
9C2 x 10C2 isn't a lot of counting.
It's a lot of counting if you apply a medieval method, sure.
anyway. i have another question
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?
I think we can assume you are wrong, yes; you can post an outline of your method for assessment, if you want.
i can explain how i derive mine. by doing the board from 1x1, 2x2,3x3, 4x4, it produces the answer
1x1 -> 0
2x2-> 4 3x3-> 16 4x4-> 36
Firstly, a square is a type of rectangle.
which follows a pattern of \[(2n-2)^{2}\]
my question stats that: think of the best way of specifying a rectangle. therefore i can decide whether to include squares as rectangles.
states*
for my benefit in this case i chose not to.
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 \[1^3 + 2^3 + 3^3 + ... + ... n^3 \]
Firstly, you cannot decide a square isn't a rectangle. And second, your answer is still wrong.
why is a square a rectangle?
all squares are rectangles; but not all rectangles are squares.
rectangle = opposites sides are the same; and 4, 90 degree corners
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.
Just a note - there was a typo above -> 3x3 gives 36 not 37.
actually a rectangle is a shape that has 2 equal sides.
which makes square also a rectangle. ok i had that clarified thanks.
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.
a parallelogram is also a rectangle
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.
ok i'm sorry. i googled that and it told me that a parallelogram is a rectangular. guess it came out wrong.
3*3=36. HOW?
*facepalm*
its 1^3 + 2^3 + 3^3
LOL. and newton who are you anyway? ^^
IF IT IS 3^3 THEN ANSWER IS 27 NOT 36???
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.
at leat no mistakes that anyone has lived to tell about ;)
LOL. are you a lecturer? >.>
YOU R SAYING IT IS NOT A MISTAKE? FUNNY
how do you remove see out of this conversation?
btw newton. can you help me in 8x9 rectangles?
ANY THING WRONG HOLYX?????????????
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.
8 by 9*
Ugh, LaTeX fail: \[^{10}C_2 \]**
you mean 8!/(8-r)!r!
wait im thinking. lol
i dont get it. why 10c2. x 9c2. why do you need to multiply.
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
Ugh, I mixed up vertical and horizontal in each part, but hopefully it made sense.
ok yea. 9c2 x 9c2 gives the same aswer 1296!
:)
omg. you're damn smart. how did you thought of that. -,- wtf.
anyway thanks for answering my question (:

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