50th word of SCOTLAND in dictionary?

Key idea: Arrange letters alphabetically and use lexicographic (factorial) counting to find the 50th permutation.

Sorted letters: A C D L N O S T. Total permutations = 8! = 40320, so the 50th permutation exists.

1. First letter: each fixed first letter gives 7! = 5040 permutations. Since 50 ≤ 5040, the first letter is A.

2. Second letter: remaining letters C D L N O S T, each fixed second letter gives 6! = 720 permutations. Since 50 ≤ 720, the second letter is C.

3. Third letter: remaining D L N O S T, each fixed third letter gives 5! = 120 permutations. Since 50 ≤ 120, the third letter is D.

4. Fourth letter: remaining L N O S T, each fixed fourth letter gives 4! = 24 permutations. Subtract blocks until position falls inside a block: 50 − 24 = 26 (after L), 26 − 24 = 2 (after N), so the 50th falls in the third block, therefore fourth letter is O.

5. Fifth letter: remaining L N S T, each fixed fifth letter gives 3! = 6 permutations. Position within this A C D O block is 2, which is ≤ 6, so fifth letter is L.

6. Sixth letter: remaining N S T, each fixed sixth letter gives 2! = 2 permutations. Position is 2, so sixth letter is N (it falls in the second 2-permutation block).

7. Last two letters: remaining letters are S and T in alphabetical order. The two permutations are: first S then T (gives ACDOLNST) and second T then S (gives ACDOLNTS). Since our position within this final block is 2, the last two letters are T then S.

Answer: ACDOLNTS