As a public service, I wrote a little program to calculate all the possible ability score arrays using 22-point buy. You can find it here: Dungeons & Dragons, 4th Edition: All Ability Score Arrays
But in case my site goes down, here is the full list for posterity. There are 121 unique ability score combinations.
18,14,11,10,10,8
18,14,10,10,10,9
18,13,13,10,10,8
18,13,12,11,10,8
18,13,12,10,10,9
18,13,11,11,11,8
18,13,11,11,10,9
18,13,11,10,10,10
18,12,12,12,10,8
18,12,12,11,11,8
18,12,12,11,10,9
18,12,12,10,10,10
18,12,11,11,11,9
18,12,11,11,10,10
18,11,11,11,11,10
17,16,11,10,10,8
17,16,10,10,10,9
17,15,13,10,10,8
17,15,12,11,10,8
17,15,12,10,10,9
17,15,11,11,11,8
17,15,11,11,10,9
17,15,11,10,10,10
17,14,14,10,10,8
17,14,13,12,10,8
17,14,13,11,11,8
17,14,13,11,10,9
17,14,13,10,10,10
17,14,12,12,11,8
17,14,12,12,10,9
17,14,12,11,11,9
17,14,12,11,10,10
17,14,11,11,11,10
17,13,13,13,11,8
17,13,13,13,10,9
17,13,13,12,12,8
17,13,13,12,11,9
17,13,13,12,10,10
17,13,13,11,11,10
17,13,12,12,12,9
17,13,12,12,11,10
17,13,12,11,11,11
17,12,12,12,12,10
17,12,12,12,11,11
16,16,13,11,10,8
16,16,13,10,10,9
16,16,12,12,10,8
16,16,12,11,11,8
16,16,12,11,10,9
16,16,12,10,10,10
16,16,11,11,11,9
16,16,11,11,10,10
16,15,14,11,10,8
16,15,14,10,10,9
16,15,13,13,10,8
16,15,13,12,11,8
16,15,13,12,10,9
16,15,13,11,11,9
16,15,13,11,10,10
16,15,12,12,12,8
16,15,12,12,11,9
16,15,12,12,10,10
16,15,12,11,11,10
16,15,11,11,11,11
16,14,14,13,10,8
16,14,14,12,11,8
16,14,14,12,10,9
16,14,14,11,11,9
16,14,14,11,10,10
16,14,13,13,12,8
16,14,13,13,11,9
16,14,13,13,10,10
16,14,13,12,12,9
16,14,13,12,11,10
16,14,13,11,11,11
16,14,12,12,12,10
16,14,12,12,11,11
16,13,13,13,13,9
16,13,13,13,12,10
16,13,13,13,11,11
16,13,13,12,12,11
16,13,12,12,12,12
15,15,15,11,10,8
15,15,15,10,10,9
15,15,14,13,10,8
15,15,14,12,11,8
15,15,14,12,10,9
15,15,14,11,11,9
15,15,14,11,10,10
15,15,13,13,12,8
15,15,13,13,11,9
15,15,13,13,10,10
15,15,13,12,12,9
15,15,13,12,11,10
15,15,13,11,11,11
15,15,12,12,12,10
15,15,12,12,11,11
15,14,14,14,10,8
15,14,14,13,12,8
15,14,14,13,11,9
15,14,14,13,10,10
15,14,14,12,12,9
15,14,14,12,11,10
15,14,14,11,11,11
15,14,13,13,13,9
15,14,13,13,12,10
15,14,13,13,11,11
15,14,13,12,12,11
15,14,12,12,12,12
15,13,13,13,13,11
15,13,13,13,12,12
14,14,14,14,12,8
14,14,14,14,11,9
14,14,14,14,10,10
14,14,14,13,13,9
14,14,14,13,12,10
14,14,14,13,11,11
14,14,14,12,12,11
14,14,13,13,13,11
14,14,13,13,12,12
14,13,13,13,13,13
One could create a random character that was worth exactly 22 points by selecting an array at random. Interestingly, 121 is 11 squared, so you could do it by rolling 1d11 x 11 + 1d11 - 11. (To make a 1d11, just roll 1d12 and re-roll 12's.)
If anyone notices any errors in the list please post here. It is very possible that there is a bug in the program.
-- 77IM
But in case my site goes down, here is the full list for posterity. There are 121 unique ability score combinations.
18,14,11,10,10,8
18,14,10,10,10,9
18,13,13,10,10,8
18,13,12,11,10,8
18,13,12,10,10,9
18,13,11,11,11,8
18,13,11,11,10,9
18,13,11,10,10,10
18,12,12,12,10,8
18,12,12,11,11,8
18,12,12,11,10,9
18,12,12,10,10,10
18,12,11,11,11,9
18,12,11,11,10,10
18,11,11,11,11,10
17,16,11,10,10,8
17,16,10,10,10,9
17,15,13,10,10,8
17,15,12,11,10,8
17,15,12,10,10,9
17,15,11,11,11,8
17,15,11,11,10,9
17,15,11,10,10,10
17,14,14,10,10,8
17,14,13,12,10,8
17,14,13,11,11,8
17,14,13,11,10,9
17,14,13,10,10,10
17,14,12,12,11,8
17,14,12,12,10,9
17,14,12,11,11,9
17,14,12,11,10,10
17,14,11,11,11,10
17,13,13,13,11,8
17,13,13,13,10,9
17,13,13,12,12,8
17,13,13,12,11,9
17,13,13,12,10,10
17,13,13,11,11,10
17,13,12,12,12,9
17,13,12,12,11,10
17,13,12,11,11,11
17,12,12,12,12,10
17,12,12,12,11,11
16,16,13,11,10,8
16,16,13,10,10,9
16,16,12,12,10,8
16,16,12,11,11,8
16,16,12,11,10,9
16,16,12,10,10,10
16,16,11,11,11,9
16,16,11,11,10,10
16,15,14,11,10,8
16,15,14,10,10,9
16,15,13,13,10,8
16,15,13,12,11,8
16,15,13,12,10,9
16,15,13,11,11,9
16,15,13,11,10,10
16,15,12,12,12,8
16,15,12,12,11,9
16,15,12,12,10,10
16,15,12,11,11,10
16,15,11,11,11,11
16,14,14,13,10,8
16,14,14,12,11,8
16,14,14,12,10,9
16,14,14,11,11,9
16,14,14,11,10,10
16,14,13,13,12,8
16,14,13,13,11,9
16,14,13,13,10,10
16,14,13,12,12,9
16,14,13,12,11,10
16,14,13,11,11,11
16,14,12,12,12,10
16,14,12,12,11,11
16,13,13,13,13,9
16,13,13,13,12,10
16,13,13,13,11,11
16,13,13,12,12,11
16,13,12,12,12,12
15,15,15,11,10,8
15,15,15,10,10,9
15,15,14,13,10,8
15,15,14,12,11,8
15,15,14,12,10,9
15,15,14,11,11,9
15,15,14,11,10,10
15,15,13,13,12,8
15,15,13,13,11,9
15,15,13,13,10,10
15,15,13,12,12,9
15,15,13,12,11,10
15,15,13,11,11,11
15,15,12,12,12,10
15,15,12,12,11,11
15,14,14,14,10,8
15,14,14,13,12,8
15,14,14,13,11,9
15,14,14,13,10,10
15,14,14,12,12,9
15,14,14,12,11,10
15,14,14,11,11,11
15,14,13,13,13,9
15,14,13,13,12,10
15,14,13,13,11,11
15,14,13,12,12,11
15,14,12,12,12,12
15,13,13,13,13,11
15,13,13,13,12,12
14,14,14,14,12,8
14,14,14,14,11,9
14,14,14,14,10,10
14,14,14,13,13,9
14,14,14,13,12,10
14,14,14,13,11,11
14,14,14,12,12,11
14,14,13,13,13,11
14,14,13,13,12,12
14,13,13,13,13,13
One could create a random character that was worth exactly 22 points by selecting an array at random. Interestingly, 121 is 11 squared, so you could do it by rolling 1d11 x 11 + 1d11 - 11. (To make a 1d11, just roll 1d12 and re-roll 12's.)
If anyone notices any errors in the list please post here. It is very possible that there is a bug in the program.
-- 77IM