Why 22 and 41 can only be in base 7 when it's true that 22 could also be in base 3?

Question

I would like to know how the solution for this word problem was attained.I couldn't get why 22 and 41 can only be in base 7 while it's true that 22 could also be in base 3.

Answer 1

Notice that Zios and Zepts have $3$ and $7$ legs.

Therefore, any number of legs that the creatures count needs to be of the form $3a+7b$.

We have that $22_3$ is $8$, but $22_7$ is $16$.

We can express $16$ as $3$ Zios + $1$ Zept, while $8$ cannot be expressed as such.

Therefore, we can effectively rule out counting $8$ legs.

Answer 2

$41$ cannot be in base $3$ since only digits in base $3$ are $0,1,2$ not $4$.

Answer 3

$22$ in base $3$ is $8$ legs...