brains and brawn
Mental acuity or intelligence and great power or physical strength, considered together. Our star football player got into an Ivy League school because he has brains and brawn. Look, kid, you need brains and brawn to make it in this world. Don't drop out of school. I know you like to go to the gym, but read a book once in a while! Brains and brawn are both important.
brains versus brawn
Mental acuity or intelligence in contrast to great power or physical strength. This isn't a case of brains versus brawn—you need both intelligence and physical strength in a situation like this. A: "OK, if it were brains versus brawn, which guy would you pick?" "B: "Oh, brains, definitely. I find nerdy guys to be very attractive." A: "Wait, the star of the football team got into an Ivy League school?" B: "Yep, it's not a case of brains versus brawn with that guy."
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