Basically it all comes down to either having a computer brain or prophetic foresight. Or just luck. I would usually just reset until I got a setup that looked doable (lots of 6s, maybe 0s, not too many locked ones clustered). Just start from the ones you know have to go in a given spot and work from there. If you happen to pick the right sequence of placements, you’ll get the badge.
Just try maybe once a day until you get it. Three minutes of your time isn’t that much.