Counting Numbers in a Range
Asked how many numbers run from 7 to 15, most people subtract and answer 8. The true answer is 9, because subtraction counts the gaps between numbers rather than the numbers themselves.
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Asked how many numbers run from 7 to 15, most people subtract and answer 8. The true answer is 9, because subtraction counts the gaps between numbers rather than the numbers themselves.
Asked how many numbers run from to , most people subtract and answer . The true answer is . Subtraction counts the gaps between numbers, not the numbers themselves — and that single mismatch is behind a whole family of test questions.
From to , including both ends: . Strictly between and , excluding both: .
The wording decides which rule applies. "From … to …" and "inclusive" keep the endpoints; "between" throws both away. The two answers always differ by exactly .
The subtraction measured the four gaps. The first number sits before any gap begins, so it never got counted. Add to include it.
This is the fence-post idea: a fence with five posts has only four spaces between them. Posts always outnumber gaps by one.
How many whole numbers are there from to , including both?
Check by listing: . Nine of them, as the rule promised.
How many whole numbers lie strictly between and ?
A quick cross-check: the inclusive count was , and dropping the two endpoints leaves . The two rules agree, as they must.
| Wording | Endpoints | Formula |
|---|---|---|
| "from to " | Included | |
| "inclusive" | Included | |
| "between and " | Excluded |