For each of the following problems briefly describe an algorithm that solves the problem, identify a good operation fundamental to the algorithm that could be used to calculate the algorithms efficiency, succinctly describe the size of the problem, and state the number of times the fundamental operation occurs as a function of the problem size in the best case and worst case. For example, if the problem was guess the secret number in the Hi-Lo Guessing Game your answer might be start at 1 as my first guess and keep adding one to my guess until I guess the number; announce my guess; the highest possible numbercall it N; best case 1 time, worst case N times.

1) Computing N! for a given N.

2) Computing the sum of the numbers 1 to N, for a given N.

3) Multiplying two N N matrices.