Compute the number of distinct paths not passing through point (2,2,2) that travel from point (0,0,0) to (4,4,4) in 12 steps, increasing a coordinate by 1 at each step.
Guest was right for the first part, but the number of ways to pass through the point (2, 2, 2) is not 6!2!2!2!, it's (6!2!2!2!)2=8100, so the answer is 26550
+92 
