CareerCup

You have a guy who is walking on a street with "X" doors on one side
(say left side).From the third round, He has to walk "X" rounds to and
fro( from point A, starting point to B, ending point).
So he walks "X" times from A to B, and back "X" times.
First two rounds he just walks to and fro.

Every time he walks he closes the particular doors corresponding to
the number of the round of his walk, starting from the third round. So
at the third round, he closes the third door, sixth door, ninth door,
.... upto
"X", if "X" is a multiple of 3,
"X-1", if "X-1" is a multiple of 3
AND
"X-2", if "X-2" is a multiple of 3

Then he walks till the "X" door. This he does for every round, till
the "Xth" round.

So, if X is 300, he walks upto the 300th door, closes the 300th door
and returns.
If X is 400, he closes upto 399th door, goes till the 400th door and returns.
If X is 500, he closes upto 498th door, goes till the 500th door and returns.

While returning, he just does nothing. He just returns to where he
started i.e. POINT A.

Likewise for the fourth round, where he close doors that are multiples
of 4 i.e. 4, 8, 12, 16, etc till X (Similar calc as in the 3rd round,
except that we consider multiples of 4 here).

And so on till the "Xth" round.

I.E.
This continiues till "X" rounds. So, from 3 to X rounds. Note that we
have not included 1st and 2nd rounds.

Problem here is:

Write the code in any language of your choice to find:
What is the minimum number of the round where he would not have to close any door?