The Parade That Never Lines Up

A marching band director tries arranging her musicians in equal rows and keeps failing by exactly one: rows of 2 2 leave 1 1 musician over, rows of 3 3 leave 2 2 , rows of 4 4 leave 3 3 , and so on — for every row size from 2 2 up to 10 10 , the leftover is one less than the row size. What is the smallest possible number of musicians?

Answer

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