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A choice that is easily made.

Example: Mike was invited to go swimming in the pool. It was very hot outside and he wanted to cool off, so it was a no-brainer for him, he promptly accepted.
* I wanted to work on my car today, but it's outside and it's raining out there. I could still do it, or I could just stay inside and wait for better weather tomorrow. It's a no-brainer, I'll wait for better weather. 
Note: The origins for most common idioms cannot be said with a certainty. What's provided, sometimes, are theories that may be plausible to how a phrase originated, but not necessarily so. If no theories are listed, then I'll usually try to provide a quote of the earliest known citation of a phrase.

In addition, quotes that contain a phrase may be taken from old newspapers, poems, or books that were written centuries ago. Just because I quote an old newspaper from, say, 1835, does not mean the phrase originates in that year. The quote is there to give you an idea on at least how old the phrase is.

N-Letter Sayings  |  Know Your Phrase - The Meanings and Origins For Phrases and Common Idioms
N-Letter Sayings
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Phrases and Idioms
Obviously we need a brain to think and reason on things. Some choices, though, are considered to be so easy, that you don't even need to think that much about them before reaching a decision. A choice like this is sometimes called a 'no-brainer.'

The origins of this phrase don't seem to be that old. I say this because I could only find it in writing from about 60 years ago. For example, in the Lethbridge Herald newspaper from the year 1968, there's a part from it that reads like so:

    "He'd break in on a goalie and the netminder would make one of those saves that our manager-coach, 
     Sid Abel, calls 'a no-brainer.' "