If you give me a synthetic puzzle to solve I wouldn't bother applying to your organization. It's much better to craft a problem to the specific domain that your company is dealing with. Then you can test for both domain expertise and problem solving ability in one fell swoop with the extra bonus of it not seeming pointless.
† The important addendum on this is that you're not going to have the top level of folks sending out blind applications unless that person is in the process of making a lateral jump into another sub-field. And even then probably not. But if you give a top applicant a synthetic puzzle after your recruiting contacts them, expect a large portion of them to thumb their nose at you. Similar note on top folks, though this is mostly pedantry -- the top OSS projects aren't on GitHub and similar. The largest and most prestigious of the OSS projects host their repos themselves.