The original problem, set in 1954 at the University of Cambridge, looked for Solutions of the Diophantine Equation x3+y3+z3=k, with k being all the numbers from one to 100. Beyond the easily found small solutions, the problem soon became intractable as the more interesting answers—if indeed they existed—could not possibly be calculated, so vast were the numbers required. But slowly, over many years, each value of k was eventually solved for (or proved unsolvable), thanks to sophisticated techniques and modern computers—except the last two, the most difficult of all; 33 and 42. Professors Booker and Sutherland's solution for 42 would...