The word oxyphenbutazone is the highest-pointed available word in the game Scrabble. If a Scrabble custom dictionary is made only from the letters in the word oxyphenbutazone , then the word oxyphenbutazone will appear in the -th in the dictionary. If , find .
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The word Oxyphenbutazone has 12 identical letters inside it, which is A, B, E, H, N, O, P, T, U, X, Y, and Z in alphabetical order. Since E, N, and O appears twice, then 1 5 − 3 = 1 2 because we can't use 2 identical letters twice, which caused repetition.
So, the available word orders are =
A _ _ _ _ _ _ _ _ _ _ _ _ _ _ = 14!
B _ _ _ _ _ _ _ _ _ _ _ _ _ _ = 14!
E _ _ _ _ _ _ _ _ _ _ _ _ _ _ = 14!
H _ _ _ _ _ _ _ _ _ _ _ _ _ _ = 14!
N _ _ _ _ _ _ _ _ _ _ _ _ _ _ = 14!
OA _ _ _ _ _ _ _ _ _ _ _ _ _ = 13!
OB _ _ _ _ _ _ _ _ _ _ _ _ _ = 13!
OE _ _ _ _ _ _ _ _ _ _ _ _ _ = 13!
OH _ _ _ _ _ _ _ _ _ _ _ _ _ = 13!
ON _ _ _ _ _ _ _ _ _ _ _ _ _ = 13!
OO _ _ _ _ _ _ _ _ _ _ _ _ _ = 13!
OP_ _ _ _ _ _ _ _ _ _ _ _ _ = 13!
OT _ _ _ _ _ _ _ _ _ _ _ _ _ = 13!
OU _ _ _ _ _ _ _ _ _ _ _ _ _ = 13!
OXA _ _ _ _ _ _ _ _ _ _ _ _ = 12!
OXB _ _ _ _ _ _ _ _ _ _ _ _ = 12!
OXE _ _ _ _ _ _ _ _ _ _ _ _ = 12!
OXH _ _ _ _ _ _ _ _ _ _ _ _ = 12!
OXN _ _ _ _ _ _ _ _ _ _ _ _ = 12!
OXO _ _ _ _ _ _ _ _ _ _ _ _ = 12!
OXP _ _ _ _ _ _ _ _ _ _ _ _ = 12!
OXT _ _ _ _ _ _ _ _ _ _ _ _ = 12!
OXU _ _ _ _ _ _ _ _ _ _ _ _ = 12!
OXX _ _ _ _ _ _ _ _ _ _ _ _ = 12!
OXYA _ _ _ _ _ _ _ _ _ _ _ = 11!
OXYB _ _ _ _ _ _ _ _ _ _ _ = 11!
OXYE _ _ _ _ _ _ _ _ _ _ _ = 11!
OXYH _ _ _ _ _ _ _ _ _ _ _ = 11!
OXYN _ _ _ _ _ _ _ _ _ _ _ = 11!
OXYO _ _ _ _ _ _ _ _ _ _ _ = 11!
OXYPA _ _ _ _ _ _ _ _ _ _ = 10!
OXYPB _ _ _ _ _ _ _ _ _ _ = 10!
OXYPE _ _ _ _ _ _ _ _ _ _ = 10!
OXYPHA _ _ _ _ _ _ _ _ _ = 9!
OXYPHB _ _ _ _ _ _ _ _ _ = 9!
OXYPHEA _ _ _ _ _ _ _ _ = 8!
OXYPHEB _ _ _ _ _ _ _ _ = 8!
OXYPHEE _ _ _ _ _ _ _ _ = 8!
OXYPHEH _ _ _ _ _ _ _ _ = 8!
OXYPHENA _ _ _ _ _ _ _ = 7!
OXYPHENBA _ _ _ _ _ _ = 6!
OXYPHENBB _ _ _ _ _ _ = 6!
OXYPHENBE _ _ _ _ _ _ = 6!
OXYPHENBH _ _ _ _ _ _ = 6!
OXYPHENBN _ _ _ _ _ _ = 6!
OXYPHENBO _ _ _ _ _ _ = 6!
OXYPHENBP _ _ _ _ _ _ = 6!
OXYPHENBT _ _ _ _ _ _ = 6!
OXYPHENBUA _ _ _ _ _ = 5!
OXYPHENBUB _ _ _ _ _ = 5!
OXYPHENBUE _ _ _ _ _ = 5!
OXYPHENBUH _ _ _ _ _ = 5!
OXYPHENBUN _ _ _ _ _ = 5!
OXYPHENBUO _ _ _ _ _ = 5!
OXYPHENBUP _ _ _ _ _ = 5!
OXYPHENBUTAA _ _ _ = 3!
OXYPHENBUTAB _ _ _ = 3!
OXYPHENBUTAE _ _ _ = 3!
OXYPHENBUTAH _ _ _ = 3!
OXYPHENBUTAN _ _ _ = 3!
OXYPHENBUTAP _ _ _ = 3!
OXYPHENBUTAT _ _ _ = 3!
OXYPHENBUTAU _ _ _ = 3!
OXYPHENBUTAO _ _ _ = 3!
OXYPHENBUTAX _ _ _ = 3!
OXYPHENBUTAY _ _ _ = 3!
OXYPHENBUTAZA _ _ = 2!
OXYPHENBUTAZB _ _ = 2!
OXYPHENBUTAZE _ _ = 2!
OXYPHENBUTAZH _ _ = 2!
OXYPHENBUTAZN _ _ = 2!
O X Y P H E N B U T A Z O A = 1 !
O X Y P H E N B U T A Z O B = 1 !
O X Y P H E N B U T A Z O E = 1 !
O X Y P H E N B U T A Z O H = 1 !
O X Y P H E N B U T A Z O N A = 1
O X Y P H E N B U T A Z O N B = 1
O X Y P H E N B U T A Z O N E = 1
Hence the right answer is 4 9 6 9 3 6 0 2 8 3 6 4 + ( 4 9 6 9 3 6 0 2 8 3 6 5 m o d 9 = 6 ) = 4 9 6 9 3 6 0 2 8 3 7 0