Balanced Distribution Of Items
You haven't quite defined your problem, so let me answer a more concrete one: when can there be an evenly spaced solution. I assume that by "evenly spaced" you mean that all the spaces are the same, and that there must be hooks and the first and last positions. If the space is $s$, then we must have
$$ L = 1 + (s+1)(H-1), $$
since the string is of the form $H(o^sH)^{H-1}$. This is possible if and only if $H-1$ divides $L-1$, in which case the spacing is
$$
 s = \frac{L-1}{H-1} - 1.
$$
In your case, 14 doesn't divide 37, so an even spacing is impossible.