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A lot of hamsters won't eat pellets, not knowing which food you use it's hard to say for sure but the pellets are often alfalfa or grass & hams just don't like them so I wouldn't really class that as picky eating.
Ideally you want them to eat everything in the mix so feeding the best quality mix you can is the best thing, not sure where you are but most people in the UK feed Syrians Harry Hamster, some hams will still get picky with some bits in that but most seem to do well on it.