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1.
Try to solve the problem with unorthodox methods. Consider any idea, no matter how unusual.
Solving the difficult riddle required ideas that came from thinking outside of the box.
by Diggity Monkeez February 15, 2005
 
2.
Old - Phrase in office-speak suggesting the use of unorthodox approaches to solve otherwise difficult problems. Not a bad phrase, but too many pointy-haired-boss types latched on to it and used it as a knee-jerk response when asked for input, thus blanching it of all meaning.

New - Happy-hour phrase meaning "Get your mind off the poontang - we're talking sports now!"
Old - Cube Monkey: Boss, I'd like your input on this problem.
Boss: Think outside of the box, Monkey.
Cube Monkey: Well, I thought you may have some time-saving insight, since you're paid to be my professional superior and all...
Boss: Just think outside of the box, Monkey!
Cube Monkey: Right. Hey! I'll use the fuckyoubossoscope!
Boss: There you go, Monkey!

New - Guy 1: Think the Rams have a chance this year?
Guy 2: It'll be tough, but anybody can make the playoffs in the NFC... What do you think, Trey?
Guy 3: Did you see the ass on that marketing intern? Damn! I could write a poem about that ass!
Guy 1: Hey, Trey... we're over here... football conversation?
Guy 2: Yeah, Trey - Think outside of the box!
by The Evil Steve August 30, 2005
 
3.
An unoriginal phrase/cliche following a conventional way of thinking used to encourage original thought and unconventional thinking, asking you do challenge the paradigm in a phrase that doesn't challenge the paradigm. Saying "Think Outside of the Box" is "Thinking Inside of the Box". This is similar in this aspect to the phrase "avoid cliches like the plague", warning against using cliches through the use of a cliche.
Boss: THINK OUTSIDE OF THE BOX, PEOPLE!
Employee: (quietly) Okay, since you're obviously not...

Jack: THINK OUTSIDE OF THE BOX!1
Ellen: Yeah, that's good advice. Maybe you should take it.
by 1pro3u January 12, 2014