95% of Singapore's population lives in apartment buildings of some kind, which pack tens if not hundreds of households into each post code.

Apparently there’s no more than 999,999 unique residences?

Singapore is a city-state on an island that is ~40x20 km in size. If you divided that rectangle evenly to a million plots, you'd end up squares that have ~30m sides. And that's before you consider that the island is not square, and that there are roads, airports, parks and things like that.

No, there are not anywhere near a million unique buildings. Instead, there are ~9000 high-rises.

1,000,000 if the code 000000 counts

In Singapore they're always 6 digits.