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The American Heritage Dictionary of Idioms » think through
think through
think through idiom
Also,
think out. Arrive at a thorough understanding of; devise or contrive thoroughly. For example, That answer doesn't work; I don't believe you've thought the problem through, or He thought out a far more efficient method. The first term dates from the early 1900s, the variant from the mid-1800s. Also see think up.
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.
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