Scrabble's Word Dictionary

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 X X -th in the dictionary. If X m o d 9 = Y X \bmod 9 = Y , find X + Y X + Y .

496936028363 496936028370 496936028364 496936028366 496936028368 496936028365 496936028367 496936028369

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1 solution

Richard Christian
Feb 17, 2015

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 15 3 = 12 15-3=12 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 ! OXYPHENBUTAZOA _ = 1!

O X Y P H E N B U T A Z O B = 1 ! OXYPHENBUTAZOB _ = 1!

O X Y P H E N B U T A Z O E = 1 ! OXYPHENBUTAZOE _ = 1!

O X Y P H E N B U T A Z O H = 1 ! OXYPHENBUTAZOH _ = 1!

O X Y P H E N B U T A Z O N A = 1 OXYPHENBUTAZONA = 1

O X Y P H E N B U T A Z O N B = 1 OXYPHENBUTAZONB = 1

O X Y P H E N B U T A Z O N E = 1 OXYPHENBUTAZONE = 1

Hence the right answer is 496936028364 + ( 496936028365 m o d 9 = 6 ) = 496936028370 496936028364+ (496936028365 mod 9 = 6) = 496936028370

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