fierce ginkgo
try n = 5
number of ways to arrange is 5!
there is only one case in which you can guess the correct order
you can also win if your guess is the right order with two things that should be swapped
e.g. you could have items 2 and 5 the wrong way round or 5 and 2 the wrong way round but one swap solves the issue
the number of pairs we can choose from 5 is 10 (the order does not matter)
so number of ways to win is 1+10 = 11
11/5! = 9.16%
for n=6,
(1+6C2)/6! = 2.22%
n=7
(1+7C2)/7! = 0.43%
so its 7
polar kite