MathDB

Fred the Four-Dimensional Fluffy Sheep is walking in 4-dimensional space. He starts at the origin. Each minute, he walks from his current position

(a_1, a_2, a_3, a_4)

to some position

(x_1, x_2, x_3, x_4)

with integer coordinates satisfying (x_1-a_1)^2 + (x_2-a_2)^2 + (x_3-a_3)^2 + (x_4-a_4)^2 = 4 \text{and} |(x_1 + x_2 + x_3 + x_4) - (a_1 + a_2 + a_3 + a_4)| = 2. In how many ways can Fred reach

(10, 10, 10, 10)

after exactly 40 minutes, if he is allowed to pass through this point during his walk?

Problem Statement