Hi Johnny,
If you are talking about a 26 foot square room (around 64m squared), two would be ideal, although with your proposed layout there would be some overlap between the maximum permissible smoke detection radii (7.5m) as set by the regulations, which is perfectly fine. Better safe than sorry as they say. Also, if you want to avoid drilling unnecessary holes, then a good investment would be a stud detector/wall scanner, which will also tell you if there are any pipes or electrical cables in the area you are scanning. A worthwhile investment for future use as well. Be advised though that most will not detect through larden plaster, although I'm assuming you have skimmed boards up there. A good one that I know of is the Bosch GMS120. Hope that helps.
Cheers,
Karim