Puzzle 02 Solution

Note that this is really a question about factors. Excluding 1 as a factor, if it has an odd number of factors, the scenario will be as such:

CLOSE (factor #1)
OPEN (factor #2)
CLOSE (factor #3)
...
OPEN (factor #2k), k is an integer
CLOSE (factor #2k+1)

so it will be closed.

If, excluding 1, it has an even number of factors, every 2 sets of its factors will mean a CLOSE-OPEN action, so it will end up as opened Only square numbers have an even number of factors, excluding 1.

Thus, the solution is the number of square numbers between 1-2006.

Answer: 44.