A frog started from the origin of the coordinate plane and made three jumps. Each time the frog jumped a distance of 5 units and landed at a point with integer coordinate. How many different possibilities of the final position of the frog are there?
I've tried to write some programs to calculate it, on khanAcademy: https://www.khanacademy.org/computer-programming/speed-optimization-of-happy-frog-jumping-everywhere/5425374405623808 and the result of each jumps is given like this: 12 73 264 553 916,
also I notice that the final position of the frog forms a decagon on the coordinate plane.
Thus, I know that the answer is 264, but I want to know what is the method to count it by hand?