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.