What is the fewest straight lines with which you can make exactly 100 squares?
For example with four vertical and five horizontal lines, evenly spaced, 20 squares are formed: twelve 1x1, six 2x2 and two 3x3.
(In reply to solution and discussion
For a rectangle m*n , i.e. m+1 by n+1 lines the number of squares can be obtained from the following formula:
This equation can be easily obtained by evaluation and simplification of
SUM ( (m-i)*(n-i)) taken over i=0 to i=n-1
Edited on May 3, 2006, 12:47 am