Translation:These buildings have colorful walls.
Because the walls are not a common property of all the buildings together. Usually every building has its own walls.
It is a very strange rule indeed, but if there are different owners, where each one has its own property, you have to set the property into the singular form, thats why "az épületeknek a fala".
If you use "az épületeknek a falai" it turns into the meaning, that the named walls are part of all the buildings together, which might be possible, but surely as a little architectonian anomaly ;-)
A betegeknek az arca sápadt - The faces of the patients are pale.
(Each patient has his own face! Using "arcai" would mean, that some faced would be shared!)
A little correction to that. If you put the possessed in plural, it is not necessarily shared but it will mean that each has more than one. With singular, it is each their own one.
"Gyerekek, emeljétek fel a kezeteket!" - Children, raise your hands - one hand each!
"Gyerekek, emeljétek fel a kezeiteket!" - Children, raise (both of) your hands.
I would slightly adjust my statement here by saying that when the possessed is singular, it is not specified if each has one or more. "A házak fala" could be one or more walls to each house. Of course, with walls, we usually understand multiple walls. The same is true with hands.
But when the possessed is in the plural, it is definitely more than one, to at least some of the possessors. "A házak falai" - all the walls of all the houses. "A gyerekek kezei" - all the hands of all the children.
How do you say that the buildings have just one wall Because now you have to guess one or more