i would like to know if i can put a mandarin goby in a three gallon tank with a baby damsel
Three gallons is really small even for nano. Unless you have access to a mandarin that eats prepared food its not really a good idea to put them in anything less than a 55 that's stocked with a large pod culture. In a 3 gallon it might last a fee weeks before it eventually starved. They peck and eat constantly at copepods.
As per sharkdude, they are very finnicky, and need a good sustained pod population (not to mention an extremely well established system)
Honestly I can't think of very many sw fish that is suitable for a 3 gallon system that isn't very rare or expensive.
Here are some suggestions that may work: Dracula goby (expensive), Lotilia/whitecap goby (expensive),yashagoby, trimmaor eviotagobies, barnacle blenny, yellow clown goby, red head goby, green banded goby
3 gallons? I wouldn't put anything other than a live food culture in a 3 gallon.
I have a yellow clown goby and a damsel and they are fine together.
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