Puzzle 19 -  Homework Scores

In a Matrix Algebra class there were n tests. The absent-minded professor put all the scores into an n × n matrix M in some strange order. John wants to find his total score and he knows that his scores are on the main diagonal. By paying one dollar to the professor, John can find the total sum of the entries in a square submatrix of M of John’s choice. What is the smallest sum of money that John has to pay to find out his total score?



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