Scrabble Dictionary

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Yes, censor is playable

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Found in the following dictionaries

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SOWPODS (Collins Scrabble Words)
OTCWL2014 (NASPA Word List 2014)
TWL06 (NASPA List 2006)

"Censor" Definition

noun

A person authorized to examine books, films, or other material and to remove or suppress what is considered morally, politically, or otherwise objectionable.
An official, as in the armed forces, who examines personal mail and official dispatches to remove information considered secret or a risk to security.
One of two officials in ancient Rome responsible for taking the public census and supervising public behavior and morals.
One that condemns or censures.
Psychology The agent in the unconscious that is responsible for censorship.

verb-transitive

To examine and expurgate.

verb

To examine in order to suppress or delete anything considered objectionable .
To suppress or delete as objectionable .
Examine (a book, film, etc.) officially and suppress unacceptable parts of it.