The ''border number'' of an square is defined as the number of unit squares whose edges border the edges of the larger square. The border numbers of 1 x 1, 2 x 2, 3 x 3 ,4 x 4, and 5 x 5 squares are illustrated below. What is the border number of a 20 unit by 20 unit square?

Guest Jun 1, 2017

#1**+1 **

An n by n square will have n edges on the top row, n edges on the bottom row, n - 2 edges on the left side and n - 2 edges on the right side for a total of n + n + (n - 2) + (n - 2) = 4n - 4 edges.

For a 20 x 20 square, there will be 4(20) - 4 = 80 - 4 = 76 edges.

The border number will be 76.

geno3141
Jun 1, 2017