# Poseidon's pets

**Number Theory**Level 3

Among the surgeonfish, the number of blue ones was one half plus one third the number of the red greater than the yellow; the number of the red, one quarter plus one fifth the number of the striped greater than the yellow; the number of the striped, one sixth and one seventh the number of the blue greater than the yellow.

Among the butterflyfish, the number of blue ones was one third plus one quarter of the total red fish; the number of the red, one quarter plus one fifth the total of the striped fish; the number of the striped, one fifth plus one sixth the total of the yellow fish; the number of the yellow, one sixth plus one seventh the total of the blue fish.

What is the smallest numbers of total of the fish that live around Poseidon’s palace?