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The image at left shows four squares of a standard eight by eight checkerboard with a jumbo-sized
checker in each square. The diameter of the jumbo-sized checker matches the width (and height) of the
checkerboard square. With creative positioning, it is possible to fit more than 64 of these checkers on
an eight by eight checkerboard. What is the maximum number of COMPLETE checkers (i.e. checkers cannot
be cut) that can fit on the checkerboard without going over any edges and without stacking checkers?
Here's the math behind it. Let's use x to represent the radius of the jumbo-sized checker. The
diameter of the checker is therefore 2x as is the width (and height) of each square on the checkerboard.
The eight by eight checkerboard therefore measures 16x by 16x. The checkers in the first column in the
image above end at horizontal position 2x (the diameter of the checker). To calculate where the checkers
in the second column end, we need to determine the value of y in the image below:
Following Pythagoras' theorem: x² + y² = (2x)² therefore
y = √