If he begins climbing on the day he fell (day 1), he will get to the 3 foot mark, fall back to 1f at night; day 2-up to 4, down to 2; day 3- up to 5, down to 3; day 4 up to 6, down to 4; day 5 up to 7, down to 5; day 6 up to 8, down to 6; day 7 up to 9, down to 7, and finally on day 8, up to 10 which is the top, and he is gone.

So 8 days is correct.