These are well-established standard spacings that make construction easier and more reliable. A stud wall has to have some repeat spacing and 16 inches is convenient. It divides nicely into 8 feet, for example for sheetrock, so that the material starts and ends at a stud with no cutting. 24 inches offers the same benefit, plus also serves well for material in four foot lengths. The standardized spacing is well ingrained in building materials, like insulation, light fixture supports, etc.
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The squares are that size because most studs are set at 16 or 24 inches apart in building framing.
Studs are normally on 16 inch centerlines, so, with 16 feet being 192 inches, you would need 12 plus 1 (for the starting stud) plus 2 (for the top and bottom plates) per wall. That is 15 studs per wall. Multiply that by 4 and you get 60 studs for the room. This doing not count framing for doors and windows, nor does it count studs for the floor and ceiling. If you get 16 foot studs, you can use 8 for the caps, leaving you needing 52 studs that are 8 foot long, so you would need 26 16 foot studs to make the 52 8 foot studs. The total required studs, then, is 34 16 foot studs.
9 if the studs are on 16" center and 7 if on 24"
If there are no windows, doors or partitions in the wall and no corner walls on the end you will need 13 studs, 24 feet of bottom plate and 48 feet of top plate.
19 or 21 if you double the ones on the ends so that the cross wall has something to nail to