A combination lock requires three selections of numbers

Last updated: 7/10/2022

A combination lock requires three selections of numbers, each from 1 through 33. Suppose the lock is constructed in such a way that no number may be used twice in a row, but the same number may occur both first and third. For example, 20 13 20 would be acceptable, but 20 20 13 would not. How many different combinations are possible? To answer this question, note that some combinations will consist of three different numbers, whereas in others the first and third numbers can be the same. The total number of combinations is