[superprismatic]

Consider a list of all permutations

of the alphabet put in alphabetical

order. This list looks like this:

ABCDEFGHIJKLMNOPQRSTUVWXYZ

ABCDEFGHIJKLMNOPQRSTUVWXZY

ABCDEFGHIJKLMNOPQRSTUVWYXZ

ABCDEFGHIJKLMNOPQRSTUVWYZX

ABCDEFGHIJKLMNOPQRSTUVWZXY

ABCDEFGHIJKLMNOPQRSTUVWZYX

ABCDEFGHIJKLMNOPQRSTUVXWYZ

ABCDEFGHIJKLMNOPQRSTUVXWZY

ABCDEFGHIJKLMNOPQRSTUVXYWZ

ABCDEFGHIJKLMNOPQRSTUVXYZW

.

.

.

ZYXWVUTSRQPONMLKJIHGFECBAD

ZYXWVUTSRQPONMLKJIHGFECBDA

ZYXWVUTSRQPONMLKJIHGFECDAB

ZYXWVUTSRQPONMLKJIHGFECDBA

ZYXWVUTSRQPONMLKJIHGFEDABC

ZYXWVUTSRQPONMLKJIHGFEDACB

ZYXWVUTSRQPONMLKJIHGFEDBAC

ZYXWVUTSRQPONMLKJIHGFEDBCA

ZYXWVUTSRQPONMLKJIHGFEDCAB

ZYXWVUTSRQPONMLKJIHGFEDCBA

We have three questions:

1. What permutation immediately

precedes ABCDEFGHIJKLMNOPQZYXWVUTSR?

2. What permutation immediately

follows ABCDEFGHIJKLMNOPQZYXWVUTSR?

3. How far apart are

AZBCDEFGHIJKLMNOPQRSTUVWXY and

ZABCDEFGHIJKLMNOPQRSTUVWXY in the list?

[Guest]

1. ABCDEFGHIJKLMNOPQZYXWVUTRS

2. ABCDEFGHIJKLMNOPRQSTUVWXYZ

3. There are 601*24!-1 permutations between them.

[dark_magician_92]

1.AB.........PQZ

ABC...........PQZYX..........TRS

ABC...........PRQ.................YZ

say the former one is kth permutation then the latter will be (26!-25!)-(25!-24!)=601*24!