Brain Teasers
Mad Ade's Grid #2
Mad Ade has drawn another grid, this time it is 20 squares by 10 squares.
How many different squares and rectangles(combined figure not individual) can be found in that grid?
How many different squares and rectangles(combined figure not individual) can be found in that grid?
Answer
11550Total number of Squares/rectangles = (Summation of row numbers) * (Summation of column numbers)
Here there are 20 rows and 10 columns or vice versa. Hence, total possible squares/rectangles
= ( 20 + 19 + 18 + 17 + 16 + .... + 3 + 2 + 1 ) * ( 10 + 9 +8 + 7 + .... + 3 + 2 + 1)
= ( 210 ) * (55)
= 11550
Hence, total 11,550 different rectangles are possible.
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
Good generalisation of an often quoted problem.
No freaking way is the difficulty rating correct on this teaser!
Nice teaser!
I was actually surprised it turned out to be so easy. Worked on it for about 30 seconds before I saw how to solve it. At that point the solution was simple.
I don't know how you arrived at the formula, but I did it this way.
Given an MxN grid of squares, there are (M+1)x(N+1) corners.
Pick the upper-left corner of the upper left square. Now any corner below and to the right defines a rectangle.
There are M rows of N corners. Now move one corner to the right. There are M rows of N-1 corners. So repeating this to the right edge gives N*(N+1)/2 * M rectangles (N*(N+1)/2 is the summation of N).
Moving down one row gives N*(N+1)/2 * (M-1) rectangles. So repeating this to the bottom gives N*(N+1)/2 * M*(M+1)/2 rectangles.
20*21/2 * 10*11/2 = 210 * 55 = 11550
I was actually surprised it turned out to be so easy. Worked on it for about 30 seconds before I saw how to solve it. At that point the solution was simple.
I don't know how you arrived at the formula, but I did it this way.
Given an MxN grid of squares, there are (M+1)x(N+1) corners.
Pick the upper-left corner of the upper left square. Now any corner below and to the right defines a rectangle.
There are M rows of N corners. Now move one corner to the right. There are M rows of N-1 corners. So repeating this to the right edge gives N*(N+1)/2 * M rectangles (N*(N+1)/2 is the summation of N).
Moving down one row gives N*(N+1)/2 * (M-1) rectangles. So repeating this to the bottom gives N*(N+1)/2 * M*(M+1)/2 rectangles.
20*21/2 * 10*11/2 = 210 * 55 = 11550
To post a comment, please create an account and sign in.
Follow Braingle!