A straight line is drawn across an 8 by 8 checkerboard. What is the greatest number of 1 by 1 squares through which this line could pass?
(A) 12
(B) 14
(C) 16
(D) 11
(E) 15

## Part C: Each correct answer is worth 8.
A straight line is drawn across an 8 by 8 checkerboard. What is the greatest number of 1 by 1 squares through which this line could pass?
(A) 12
(B) 14
(C) 16
(D) 11
(E) 15

## Solution

Let's suppose that we start in square $A$ and end in square $B$. In order to achieve the maximum number of squares, we must cross seven horizontal and seven vertical lines. If we avoid going through the corners of the squares, we enter one new square for every line we cross. Thus we enter fourteen new squares for a total of fifteen squares.

![](https://cdn.mathpix.com/cropped/2024_04_20_faa9db06d997f2a5b9b1g-235.jpg?height=523&width=525&top_left_y=300&top_left_x=1361)

ANSWER: (E)

## Part C: Each question is worth 8 credits.