perlmeditation
kvale
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.
<p>
Recall that the factorial function is n! = n*(n-1)*(n-2)*...3*2*1, and
for this problem, we insist that n be an integer. floor(x)
gives the greatest integer less than or equal to x. For example, we
can write
<code>
floor(sqrt((3!)!))
= floor(sqrt(6!))
= floor(sqrt(720))
= floor(26.83...)
= 26
</code>
to obtain a Knuth expression for 26.
<p>
One could spend a pleasant afternoon manually creating Knuth expressions for small integers
with a hand calculator. But it is much more fun to write a
perl program to do this for you. The challenge is to write an elegant,
fast, or golfish program that finds Knuth expressions for the integers 1 to 10 inclusive.
<p>
I'll post my solution in a day or so.
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<p>
-Mark
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