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How many stones high are the pyramids of Giza, on the outside?
There are three pyramids, did they have a pre-determined number of stones in height? in that case was it representative of something? were they that precise?
So the 3 pyramids, what are their ratios?
How many stones high are the pyramids of Giza?
Which pyramid at Giza? They're all different.
The simple answer is Cheops is now 201 and was originally about 210, but it doesn't mean what you think it means. The layer heights were not consistent, their heights were not precise, the slopes of different pyramids were not consistent, and what we see today is not how they were built.
...on the outside?
Let's make sure everybody's clear, the pyramids are not hollow. They're built in solid layers with passages designed into them.
Was it representative of something? Were they that precise?
It was representative of the tools and system they used to measure slope, the seked. They weren't precise, they were consistent. Length is hard to reproduce consistently, but once you have the length certain (ie. everyone on the project is making copies of the same master cubit stick) slopes are easy to reproduce. The slopes and lengths within a given project would remain consistent, but could vary from project to project as each project would have slightly different ideas of the length of the cubit. So long as everyone used the same measure for cubits and palms everything would turn out fine.
Stacking a pile of rocks is pretty stable, but if you make the slope too great it will collapse. Make the slope too shallow and it takes too much material to reach a given height.
We see the earlier Bent Pyramid with a 54° slope tapering suddenly to a very conservative 43°. The Red Pyramid is built with the same very conservative 43°. The Great Pyramid is at 51°50', Khafre is at 53°10', and Menkaure is at 51°20.
Did they choose the height based on the number of stones?
No, the height was chosen by how big they could make the base and how much material they could afford.
If you want to build a pyramid to a certain height you need to know the slope and base. By the time of Giza they had settled on a safe slope of roughly 51-53°, so only the base size could vary. The higher the pyramid, the bigger the base, the more material you needed at a frightening rate. At a 52° slope adding 20% more height would double your material.
How many stones high are the pyramids of Giza, on the outside?
There's problems with this question. First, what we see today is not what was there originally. Originally the Pyramids were covered in smoothed casing stones, usually made of limestone. These high quality, valuable building materials have been mostly weathered or stolen. What we see now is the rough, interior stones.
Then, the pyramids today have lost several upper layers. It's hard to tell what their original height or number of layers were, though it can be guessed at from the slope.
The big problem is the stones were layered in varying heights. In particular base stones were much larger than the stones higher up. It only mattered that the stones within each layer were the same height. You were done when everything converged at the top.
In short, to make such a massive building project more efficient the Egyptians only used as much precision and consistency as was necessary. The exact slope was not important, but it had to remain consistent through the whole project or everything would not fit together. The height of the layers was not important, but each stone in a layer had to be the same height to produce a level layer.
