Three-leggers

On a newly discovered planet live animals that astronauts named after the number of legs one-leggers, two-leggers, three-leggers, and so on (there were no animals without legs there). Animals with an odd number of legs have two heads, animals with an even number of legs have one head. In a certain hollow they met a group of such animals and counted 18 heads and 24 legs on them. How many animals could have been in the hollow? Determine all possibilities.

Final Answer:

n₁ =  10
n₂ =  12
n₃ =  14

Step-by-step explanation:

$$\begin{gathered} 18=2\cdot a+1\cdot b+2\cdot c \\ 24=1\cdot a+2\cdot b+3\cdot c \\ a,b,c\in N \\ {a}_1=2;b_1=2;c_1=6 \\ {a}_2=3;b_2=6;c_2=3 \\ {a}_3=4;b_3=10;c_3=0 \\ {n}_1=a_1+b_1+c_1=2+2+6=10 \end{gathered}$$

$n_2=a_2+b_2+c_2=3+6+3=12$

$n_3=a_3+b_3+c_3=4+10+0=14$

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