Advent calendar 2025
9 December
In a 3 by 5 grid of squares, if a line is drawn from the bottom left corner to the top right corner, it will pass through 7 squares:
In a 251 by 272 grid of squares, how many squares will a line drawn from the bottom left corner to the top right corner pass through?
Show answer & extension
Hide answer & extension
The line passes through one square in each column plus an extra square in a column whenever is passes between rows. It must pass between rows 250 times (to get from row 1 to 251) so
in total it passes through 250+272 = 522 squares.
Extension
In a 200 by 300 grid of squares, how many squares will a line drawn from the bottom left corner to the top right corner pass through?
![](javascript:showlimage("advent2025-squares.png"))