20qt is 5 gallons and would work for 3 gallon boils.
my stove will not bring a 5gallon pot to a boil. its a ceramic top stove and the wide diameter of the pot causes the element to shut off a lot, to avoid damaging the cook top.
if you have normal electric coils, or a gas range, you should be able to handle a 5gallon pot. might take a bit to heat, but it should work.
yer other option is two smaller pots, like 12qt, and split your boil between them (as well as your extract and hops...you'll need a good kitchen scale for that)
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