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To devise; to develop or invent something from one's thoughts. A noun or pronoun can be used between "think" and "up." I'm sure our R&D department will be able to think up a solution to the issue. He thought the story up while he was sailing along the coast of Spain.
Farlex Dictionary of Idioms. © 2015 Farlex, Inc, all rights reserved.
think something up
to contrive or invent something. Don't worry. I'll find a way to do it. I can think something up in time to get it done. John thought up a way to solve our problem.
McGraw-Hill Dictionary of American Idioms and Phrasal Verbs. © 2002 by The McGraw-Hill Companies, Inc.
Devise, contrive by thinking, as in She's an expert at thinking up interesting programs. [Mid-1800s]
The American Heritage® Dictionary of Idioms by Christine Ammer. Copyright © 2003, 1997 by The Christine Ammer 1992 Trust. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.
To devise or develop something: She thought up a plan to make more money. He thought the design up all by himself.
The American Heritage® Dictionary of Phrasal Verbs. Copyright © 2005 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.