(3) On the ground, there are 10 birds pecking at food, among any 5 birds, at least 4 are on a circle. How many birds are there at least on the circle with the most birds?
First, we prove that at least 5 birds are on the same circumference. If not, then the 10 birds can form $C_{10}^{5}=252$ groups of 5 birds, and each group of 5 birds has 4 birds on the same circumference. However, these 4 birds can belong to 6 different groups of 5 birds, so there should be $\frac{252}{6}=42$ different circles. These 42 different circles should have $42 \times 4=168$ birds standing on them, but there are only 10 birds in reality. Therefore, at least one bird stands on 17 different circles.

These 17 different circles, besides the common position of this bird, have another $3 \times 17=51$ birds standing on them, but there are only 9 birds left in reality. Thus, at least one bird stands on 6 different circles. This means that these two birds stand on 6 different circles together, but there are only 8 birds left, which is impossible.

Next, we prove that the circle with at least 5 birds has at least 9 birds standing on it.

Let's denote $A, B, C, D, E$ as the 5 birds standing on the same circle $C_{1}$. If the conclusion is not true, then let's denote the two birds not on $C_{1}$ as $H, K$. Then:

Since the group $\{A, B, C, H, K\}$ has 4 birds on the same circle, and $H, K$ are not on $C_{1}$, we can assume that $A, B, H, K$ are on the same circle $C_{2}$, and $C_{2} \neq C_{1}$, which means $C, D, E$ are not on $C_{2}$.

Since the group $\{C, D, E, H, K\}$ has 4 birds on the same circle, and $H, K$ are not on $C_{1}$, we can assume that $C, D, H, K$ are on the same circle $C_{3}$, and $E$ is not on $C_{3}$.

Thus, examining the group of 5 birds $\{A, C, E, H, K\}$, any 4 birds standing on the same circle leads to a contradiction, but if any 4 birds are not on the same circle, it also contradicts the assumption.

Therefore, outside the circle $C_{1}$ where $A, B, C, D, E$ stand, there can be at most 1 bird. That is, the circle with the most birds has at least 9 birds.