Eötvös 1930/2 solution

34th Eötvös 1930

Problem 2

A straight line is drawn on an 8 x 8 chessboard. What is the largest possible number of the unit squares with interior points on the line?

Solution

There are 14 internal grid lines. The line can cross each one at most once, so it can make a total of at most 14 crossings. But one crossing is required each time it changes unit square, so at most 1+14 = 15 squares. But 15 is certainly possible - take a line parallel to a main diagonal and close to it.

34th Eötvös 1930