OP, the slugs/snails did you a favour in eating the flowers off if your intention was to grow fat tubers (aka the potato). Left to pollinate, small tomato-like, mildly toxic fruit would have formed as a result, and would have diverted energy away from tuber production.
I did once sow the seeds taken from the said fruit. I did get potato plants and a potato crop but, sadly, I never got a unique genetic variation...
Last year I didn't water, got a tiny crop. I didn't dig them all up either. When I got round to weeding I found lots coming up on their own, so I fed them, mulched them and put a leaky hose round them. Coming along nicely now, I have high hopes for later on in the year.
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Gardening in Central Norfolk on improved gritty moraine over chalk ... free-draining.
I did once sow the seeds taken from the said fruit. I did get potato plants and a potato crop but, sadly, I never got a unique genetic variation...