Here is a slight hint for the “Plumbing Puzzle”:

As ‘DIY’ correctly noted in this comment, the root cause of the observed effect is that the hot water is at a higher pressure than the cold. The reason for this is that the cold water is fed from a water tank in the loft, whilst the hot water comes from the combi-boiler (which is fed directly from the water mains).

Aside:

If the mains water pressure is higher than that of the water coming from the water tank then what’s the point of having a tank? I’m not sure; I’ve yet to consult a plumber for the answer to this.

It could be a historic artefact. Maybe once upon a time the mains water pressure was not that great. Or maybe the water mains pressure is good with only one or two faucets on, but would be unable to supply all four flats in the property if everyone happened to turn on their faucets and flush the toilet at the same time? Or maybe it’s for isolation, so that someone in another flat flushing the toilet won’t make your shower go hot. (But that doesn’t really work out, because it would make your shower go cold instead, since the hot water from the combi-boiler is still fed from the cold water mains!) I don’t know.

What I do know, however, is that this isn’t the full solution to the puzzle. Even with a pressure differential, why would the hot water push back into the cold pipe rather than coming out of the faucet? Surely it's easier to come out from the faucet than to push back against the cold water?

So the question remains: How does the hot water end up in the cold water pipe?

Give up? Click here for the solution.