Brain Teasers
Rectangles
If you were to construct a 7 x 7 checkered square (i.e., a 7 x 7 chess board), how many rectangles would there be in total? You need to include squares too because a square is a special kind of rectangle.
Hint
All the rectangles on the board can be identified by connecting:2 points of the 8 in the top edge (to form the length of the rectangle) and
2 points of the 8 in the left edge (to form the breadth of the rectangle).
Answer
Length of rectangle and number of Possibilities7 units 1
6 units 2
5 units 3
... ...
1 unit 7
So, number of possibilities for different lengths of rectangles = 1 + 2 + 3 + ... + 7 = 28.
Similarly, number of possibilities for different breadths of rectangles = 1 + 2 + 3 + ... + 7 = 28.
Hence, number of rectangles = 28 x 28 = 784.
Hide Hint Show Hint Hide Answer Show Answer
What Next?
View a Similar Brain Teaser...
If you become a registered user you can vote on this brain teaser, keep track of which ones you have seen, and even make your own.
Solve a Puzzle
Comments
Great puzzle. I did it by considering a 1x1 square , a 2x2 square and a 3x3 square to which the answers were 1 , 9 (3^2) and 36(6^2).
Surprisingly the answer is the square of the associated triangular number.
Surprisingly the answer is the square of the associated triangular number.
Jan 22, 2011
you can solve this for any size board
with this equation:
(x^4+2x^3+x^2)/4
where x is the size of the board
with this equation:
(x^4+2x^3+x^2)/4
where x is the size of the board
Liked this one
To post a comment, please create an account and sign in.
Follow Braingle!