Has anyone figured out an answer for **puzzle 85**?

Here's what I got so far.
The "would be" left adjoint should look like:

$h(x) = \bigwedge \\left\\{ y \in \mathbb{N}[S] \; : \; f(y) \to x \\right\\} .$

I've tried instantiating the formula for a resource in \$$\mathbb{N}[T] \$$ – I picked \$$[\textrm{egg}]\$$ and I've used the fact that \$$f \$$ forgets bowls and shells:

$h([\textrm{egg}]) = \bigwedge \\left\\{ [\textrm{egg}], [\textrm{egg}] + [\textrm{bowl}], [\textrm{egg}] + [\textrm{shells}], [\textrm{egg}] + [\textrm{bowl}] + [\textrm{shells}], \cdots \\right\\} .$

But I cannot find an element in \$$\mathbb{N}[S] \$$ that is less than (that is, can be produced from) both \$$[\textrm{egg}] \$$ and \$$[\textrm{egg}] + [\textrm{bowl}] \$$.
I'm tempted to conclude there is no left adjoint, but I doubt my reasoning as it goes against [John's optimism](https://forum.azimuthproject.org/discussion/comment/18382/#Comment_18382).