The answer to the sums of the diagonals of a 1001 by 1001 spiral matrix is 669,171,001. More interesting than the answer is the number of responses and the variety of solutions. Beside solutions from APL and J, I received solutions using C++, RoboBasic, and EXCEL. Several submitters used their observations to produce mathematical solutions. Some of the mathematical solutions resulted in different equations. I'll try to summarize all the submissions.
/lp/association-for-computing-machinery/exercises-and-problems-solutions-to-the-diagonal-sums-on-spiral-urRAV9nUv5