Martin, the mathematical mole, has dug an extensive network of underground tunnels which he has approximated, in his magnificent mole mind, as a 3D lattice of 30 x 30 x 30 intersections. The distance between intersections is approximately constant. He is currently at intersection (20, 20, 15) and wishes to get to his secret food cache at (25, 25, 20) by one of the many shortest routes available. There are stones blocking the intersections at (21, 22, 10), (22,19,18), (22, 22, 16), (24, 18, 18) and (26, 26, 18).

From how many equally short paths can he choose?

[HINT: You could try an easier problem first.]

Author: Leslie Green