Problem #11

The noted computer scientist Donald Knuth has conjectured that every positive integer can be obtained by beginning with a single 3 and applying some combination of the factorial, square root, and floor functions. Recall that the factorial function is n! = n(n-1)(n-2)...3*2*1 [note that for this problem we insist that n be an integer] and floor(x) gives the greatest integer less than or equal to x. For example, we can write floor(sqrt((3!)!)) = floor(sqrt(6!)) = floor(sqrt(720)) = floor(26.83...) = 26 to obtain such an expression for 26.

This month's problem is to express each of the integers from 1 to 10 inclusive in this manner.

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