There is a cage with chickens, rabbits and nine-headed birds; A chicken has two legs and a head; A rabbit has four legs and a head.

Analysis: If there is only one kind of animal in the cage, there are at most 50 chickens (100ft ÷2), 25 rabbits (100ft ÷4),10/bird (100). By enumeration:

1), if there are 1 1 birds with nine heads, then there are 99 birds in total (9× 1 1), leaving 1 head, only chickens or rabbits, which is inconsistent with the meaning of the topic.

2) If there are 10 birds with nine heads (9× 10) and 20 feet (2× 10), the remaining 10 and 80 feet; Even if this 10 head is a rabbit, it is only 40 feet (4× 10), so it is impossible.

3) If there are nine birds with nine heads, there are 8 1 (9×9) heads and 18 feet (2×9), and the remaining 19 heads and 82 feet; Even if all 19 heads are rabbits, there are only 76 feet (4× 19), so it is impossible.

4) If there are eight birds with nine heads, there are 72 heads (9×8) and 16 feet (2×8), leaving 28 heads and 84 feet; If these 28 heads are chickens, they should be 56 feet (2×28), which is 28 feet short. This is because the rabbits are counted as chickens, and each rabbit is counted as 2 feet (4-2), so the original rabbit has 14 (28÷2), so it is just right to have 14. Meet the meaning of the question.

5) If there are seven birds with nine heads, there are 63 heads (9×7) and 14 feet (2×7), leaving 37 heads and 86 feet; If these 37 heads are chickens, they should be 74 feet (2×37) short of 12 feet. This is because the rabbits are counted as chickens, and each rabbit is counted as missing 2 feet (4-2), so there were originally 6 rabbits (65,438+02 ÷ 2), so there were 36,544 rabbits. Meet the meaning of the question.

6), if there are six birds with nine heads, there are 54 heads (9×6) and 12 feet (2×6), leaving 46 heads and 88 feet; Even if these 46 heads are all chickens, there are more than 88 feet (46×2=92), not to mention four-legged rabbits. So it is impossible.

7), if there are five birds with nine heads, there are 45 heads (9×5) and 10 feet (2×5), leaving 55 heads and 90 feet; Even if these 55 heads are all chickens, there are more than 90 feet (55×2= 1 10), let alone rabbits with four legs. So it is impossible.

8), ... Further down, the fewer birds with nine heads, the more heads left, that is, the more chickens or rabbits, the more unsatisfactory the number of feet. So there is no possible answer.

So the answer is: there are only 14, 14 and 8 chickens or 3 1, 6 and 7 birds in the cage respectively.

I finally finished it, and I'm sure the answer is right. Take your time!

Note: enumeration is also a way to solve the problem, but if you enumerate the possibilities of rabbits or chickens, it will be too complicated and miserable!