Predict the hybridisation and the moment

You will write three small functions of valence bond theory. One counts the unpaired electrons of a free ion. One turns a count into the spin-only moment. One names the hybridisation of an octahedral complex.

The idea. Electrons go into five orbitals one at a time, and then pair up. $\mu = \sqrt{n(n+2)}\ \text{BM}$. A strong ligand with six or fewer d electrons frees two 3d orbitals and gives $d^2sp^3$.

Your tasks.

1. Complete unpaired(d_count) so that it returns the unpaired electrons of a free ion: the count itself up to 5, and 10 minus the count after that.
2. Complete moment(n) so that it returns the spin-only moment in BM.
3. Complete hybridisation(d_count, strong) so that it returns "d2sp3" for a strong ligand with six or fewer d electrons, and "sp3d2" otherwise.