The essential factors for determining the number of spots needed in a room are probably the following:
1. What level of illumination is desired in the individual rooms? A workspace for sewing requires a completely different level of illumination than basic lighting for cozy TV watching. Other possible light sources must also be considered, e.g., an additional reading lamp.
2. What luminous efficacy (luminous flux) do the planned spots have (how many lumens)? Actually, the question should be reversed: Which spotlights are suitable for the purpose at all?
3. To calculate the resulting illumination at the location considered, further influencing factors must be taken into account:
3.a. What is the radiation characteristic of the spotlights? There is a huge difference between 120 degrees and 30 degrees beam angle; one is more of an area light, the other more of a point light, e.g., to illuminate pictures. For this, the luminous efficacy at a distance for the spotlight with a 30-degree beam angle is certainly higher (more focused) at the same power consumption, so you need many more spotlights if you want to use these for area lighting, but then you have a higher resulting illumination.
3.b. What is the ceiling height? The higher the room, the less light reaches the floor if the same spotlight is assumed.
4. What is the absorption behavior of the illuminated objects? White walls reflect a larger part of the light than furniture or floors made of dark wood.
5. How large is the area to be illuminated?
6. How evenly should the area be illuminated? Few point spotlights create bright spots at certain points; in between it is darker if they are spaced far apart. With area spotlights that may even overlap in their influence area, you certainly get a more even illumination, but this is not always desired. Perhaps you want to highlight certain objects (furniture, pictures) specifically.
(7.) Then there are also swivel versions of spotlights whose light cone can be directed within certain limits, e.g., onto a picture on the wall.
Without knowing all these factors, you actually cannot assess how best to distribute your spotlights. I am not an expert either and if in doubt would simply test with a trial spotlight on-site in the dark. The 3 spotlights you mentioned in the hallway might still work if they have about a 120-degree beam angle and each has preferably >300 lm. With <200 lm and 30-degree beam angle, however, it could get tight, or the lighting is rather spot-like as described above.
