There are 8 three-digit displays which will represent a perfect
square number, IF you consider 1:00 p.m. to be "between" 1:00 p.m.
and 5:00 p.m. Otherwise only 7.
1:00 p.m., 100 = 10²
1:21 p.m., 121 = 11²
1:44 p.m., 144 = 12²
2:25 p.m., 225 = 15²
2:56 p.m., 256 = 16²
3:24 p.m., 324 = 18²
4:00 p.m., 400 = 20²
4:41 p.m., 441 = 21²
Edwin