To count numbers between 100 and 300 (exclusive of 300, inclusive of 100 for general interpretation of 'between', but for this specific counting problem, it's typically numbers > 100 and < 300, thus 101 to 299) that begin or end with 2, we consider numbers starting with 2 and numbers ending with 2 separately, then subtract the overlap. Numbers starting with 2 are 200-299 (100 numbers). Numbers ending with 2 in the range 101-299 are 102, 112, ..., 192 (10 numbers) and 202, 212, ..., 292 (10 numbers), totaling 20 numbers. The overlap is numbers starting with 2 and ending with 2, which are 202, 212, ..., 292 (10 numbers). Using the principle of inclusion-exclusion: (Numbers starting with 2) + (Numbers ending with 2) - (Numbers starting and ending with 2) = 100 + 20 - 10 = 110.