Professor Shortcut records his grades using only his students' first and last initials. What is the smallest class size that will definitely force Prof. S. to use a different system?

The smallest size will be "677". A further explanation is given below.

Explanation:

Since the English alphabet seems to have twenty-six letters, the faculty member would prefers 2 letters very first as well as last. Professor would have had at that very many varying effects. Whilst also pigeonhole concept, whenever class size would be 677 and after that professor must be using a better or different approach.

Therefore the cheapest or smallest item seems to be "677"

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