What does Wilf mean by an "easy" vs. a "hard" problem? By a "fast" vs. a "slow" algorithm?
Write a URM program that computes the function f(x,y) = xy; then give an upper bound for the number of steps your program takes as a function of input size x+y. Try your program in the URM Simulator to see if it works, and to see if your upper bound is accurate (the Output pane in the simulator shows the number of instructions performed).
Give an upper bound for the number of steps it takes to multiply an m-digit and an n-digit natural number using the algorithm we learn in elementary school. In your answer, state what you consider as one "step".
Give an upper bound, as a function of input size m+n, for the number of steps your URM program (above) takes to multiply an m-digit and an n-digit natural number.
Prove that if HP were decidable, then Goldbach's Conjecture would be decidable. (Goldbach's Conjecture: every even number is the sum of two primes.)