5 ms·
The number of 1x1 squares on a chessboard. The number of squares on a chessboard is 204 1, 8x8 square 4, 7x7 squares 9, 6x6 squares 16, 5x5 squares 25, 4x4
by eposts 19y ago
The number of 1x1 squares on a chessboard. The number of squares on a chessboard is 204
1, 8x8 square
4, 7x7 squares
9, 6x6 squares
16, 5x5 squares
25, 4x4 squares
36, 3x3 squares
49, 2x2 squares
64, 1x1 squares
- icky 19y ago> The number of squares on a chessboard is 204 The number of squares on a chessboard is infinite, if you don't limit yourself to edges already drawn for you.
- jgrahamc 19y agoYes, and of course you should really generalize that so that the number of squares on a board with nxn single squares is sum(i=1..n) i*i
- eru 19y agoThis thread is pedantic. By thy way: sum(i=1..n) i*i = n/6 + n^2/2 + n^3/3
- jgrahamc 19y agoProof?
- hhm 19y agoThis proof helps: http://pirate.shu.edu/~wachsmut/ira/infinity/answers/sm_sq_cb.html http://pirate.shu.edu/~wachsmut/ira/infinity/answers/sm_sq_c... From that: sum bla= n(n+1)(2n+1)/6, then you go distribute
- eru 19y agoNice. How did I get the result in the first place? I know that this sum can be expressed as a cubic polynomial. So I just evaluated the sum at four data-points (n=0,1,2,3) and used those to determine the four coefficents by solving a linear equation system.