I have a head modeled and would like to cut puzzle pieces out of it following a helical path. The end results is to make a head out of puzzle pieces but have some of the pieces missing from the head. I really don't want to uvunwrap the geometry since the ear has a lot of folds. I just wish that there was someway to project a puzzle piece. Any suggestions on how I should go about doing this?

you can project images onto objects using the UV project modifier, but it requires an existing UV map. You could project a puzzle piece onto the mesh, then manually select vertices along the border and use Unwrap > Project from view. But seems really inconvenient to me...

Maybe try bProjection addon / background image + lasso selection (ctrl + LMB)?
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