Software engineer & founder of @RailsBridge and @LivableCode. Currently stirring the pot at @SalesforceUX. She/her. 
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If the company can only pick one of those (for some reason), the company should always go with a take home project and ask them about it after. This is the most realistic of them all since you often work independently at work anyway.
Picking whichever one most closely matches your current workstyle is a distant second place IMO. You’ll only hire people who are comfortable with that, which limits diversity. (And yes, with every new hire your work style might shift a bit. Teams are immutable!
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Oh absolutely. Candidates should have choice. My comment was for the companies who claim that they can't use multiple processes because of some nonsense. If they say that, then they should be encouraged to go for the take home since that is most flexible
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