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Math and Arithmetic
Geometry

How many rectangles can you build with 8 squares?

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2010-01-28 22:32:00
2010-01-28 22:32:00

Squares are actually also rectangles so you could make 8 rectangles without touching any of the squares. However, if you could cut the squares, that would be a different problem....

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16 1x1 rectangles + 12 2x1 rectangles + 8 3x1 rectangles + 4 4x1 rectangles + 12 1x2 rectangles + 9 2x2 rectangles + 6 3x2 rectangles + 3 4x2 rectangles + 8 1x3 rectangles + 6 2x3 rectangles + 4 3x3 rectangles + 2 4x3 rectangles + 4 1x4 rectangles + 3 2x4 rectangles + 2 3x4 rectangles + 1 4x4 rectangle. A Grand Total of: 100 squares and rectangles. OR: A rectangle is formed by 2 horizontal lines and 2 vertical lines. There are 5 horizontal and 5 vertical lines so the number of rectangles is 5C2 * 5C2 = 10 * 10 = 100




how many vertices does 3 hexagons and 8 rectangles have all together


All numbers equal to or less than 40.Very many:(One 40 *1 rectangle, two rectangles in 20 ways, three rectangles in a whole bunch of ways , etc) If all the squares are to be used and the rectangles are outlines (not filled) then five19 * 317 * 515 * 713 * 911 * 11If all the squares are to make a single unbroken and completely filled rectangle and the orientation of the rectangle does not matter then you can make four:40*120*210*48*5


http://jd2718.wordpress.com/2007/04/21/puzzle-how-many-rectangles-on-a-chess-board-solutions/




A chess board has 64 squares - but if you look closely, you can make another square out of every 2x2 (49), 3x3 (49) 4x4 (25) 5x5 (16) 6x6 (9) 7x7 (4) and finally one 8x8 square - so 64 + 49 + 36 + 25 + 16 + 9 + 4 + 1 = 204 squares. If we assume "rectangles" are all other rectangles that are not also squares (it could be argued that a rectangle is a square - in which case you add 204 to the number I compute here), then you can see a whole bunch more. It helps to know that 1 + 2 + 3 + ... + n = n x (n+1) / 2 (speeds up the math) 1 square tall: 2 x 1: 7 per row times 8 rows = 56 3 x 1: 6 per row ... = 48 for a total of (7+6+5+4+3+2+1) x 8 (rows) = 8 x 8 x 7 / 2 = 224 2 squares tall: (7 + 6 + ...) x 7 x 2 = 8 x 7 x 7 / 2 You can see that if we keep going we get 8 x (8 + 7 + 6 + ... + 1) x 7 / 2 = 8 x ( 8 x (8 + 1 ) / 2 ) x 7 / 2 = 2 x 8 x 9 x 7 total number of rectangles = 1008 So the answer is 204 squares and 1008 (non-square) rectangles, or 204 squares and 1212 "rectangles" (including squares).


64 squares are on a checkers board. Just count the squares!!!!!!!!!!!!!!!! -SUPERyOSHI



There are 64 squares on a chess board and you get this from the 8 times 8= 64



The most common checker board size is 8 squares by 8 squares for a total of 64 squares. There are 32 squares of each color.


64 squares are on a checkers board.


The number of square tiles is always equal to factor pairs. As an example, imagine a rectangle that contains 8 squares - 2 rows of 4. 2 X 4 = 8. In other words, the dimensions of the rectangles are ALWAYS equal to a factor pair of the number of squares in the rectangle. A rectangle containing 24 squares could be made as 24x1, 12x2, 8x3, or 6x4.


There are 64 squares as on a chess board. This is assuming that 8 by 8 in the question means 8 rows and 8 columns.


A chess board that has an 8 X 8 grid will have 64 squares .


There are 64, it is an 8 by 8 grid.


There are 8 squares in a row on a checkerboard. The full board consists of 64 squares (8×8).


The number of square tiles is always equal to factor pairs. As an example, imagine a rectangle that contains 8 squares - 2 rows of 4. 2 X 4 = 8. In other words, the dimensions of the rectangles are ALWAYS equal to a factor pair of the number of squares in the rectangle. A rectangle containing 24 squares could be made as 24x1, 12x2, 8x3, or 6x4.


8 squares x 2/3 = 16/3 squares = 5 1/3 squares


I get 204 There are 64 1x1 squares; 49 2x2 squares; 36 3x3 squares; 25 4x4 squares; 16 5x5 squares; 9 6x6 squares, 4 7x7 squares and 1 8x8 square.


8 squares per row. A chess board is made up by 8 x 8 squares.


A chess board that has an 8 X 8 grid will have 64 squares .



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