KeenObserver,
It’s actually 7 cervical + 12 thoracic + 5 lumbar (you missed those). The 5 sacral vertebrae are fused into the sacrum in adulthood, so you might count that as one bone. The coccyx is also made of several rudimentary vertebrae, which are generally fused in adulthood.
So it’s at least 24 + 1 sacrum + 1 coccyx = 26, and possibly over 30 if you count the sacral and coccygeal vertebrae separately.
From a picture on Wikipedia, it looks to me like the 7 cervical vertebrae are in the neck/by the skull (i.e., not in the back). That would leave the 12 thoracic and 5 lumbar and the sacrum/coccyx in the back… which would add up to 19 (18 if the tailbone was not considered to be in the back). Perhaps this is how our sages were counting?