Jeff caught 21 fish, each having a mass of at least $0.2 \mathrm{~kg}$. He noticed that the average mass of the first three fish that he caught was the same as the average mass of all 21 fish. The total mass of the first three fish was $1.5 \mathrm{~kg}$. What is the largest possible mass of any one fish that Jeff could have caught?
Since the total mass of the first three fish is $1.5 \mathrm{~kg}$, the average mass of the first three fish is $0.5 \mathrm{~kg}$.

Let $M$ be the total mass of all of the fish. Since the average mass of the first three fish is the same as the average mass of all of the fish, this means $\frac{M}{21}=0.5 \mathrm{~kg}$ or $M=10.5 \mathrm{~kg}$.

Since the first three fish have a total mass of $1.5 \mathrm{~kg}$, this means the last 18 fish that Jeff caught have a total mass of $10.5 \mathrm{~kg}-1.5 \mathrm{~kg}=9 \mathrm{~kg}$.

If 17 of these 18 fish have as small a mass that is as possible, the $18^{\text {th }}$ of these fish will have a mass that is as large as possible.

The smallest possible mass is $0.2 \mathrm{~kg}$, so the total mass of 17 fish, each having as small a mass as possible, is $17 \times 0.2 \mathrm{~kg}=3.4 \mathrm{~kg}$.

The largest possible mass of any fish that Jeff could have caught is $9 \mathrm{~kg}-3.4 \mathrm{~kg}=5.6 \mathrm{~kg}$.

ANSWER: $5.6 \mathrm{~kg}$