There are 48 soldiers in a parade line. Soldier M is 23rd from the front and Soldier N is 13th from the back. Find the number of soldiers between M and N.
12
This is a linear-arrangement ranking problem. The two soldiers are counted from opposite ends of the same line, so the first job is to bring both positions onto a common reference — here, position counted from the front.
The total strength of the parade line is \(48\) soldiers.
Soldier M is 23rd from the front, so M simply occupies position \(23\) when we count from the front.
Soldier N is 13th from the back. To convert a from-the-back rank into a from-the-front position, use \(\text{position from front} = \text{total} - \text{rank from back} + 1\).
So N's position from the front is \(48 - 13 + 1 = 36\).
The soldiers standing strictly between positions 23 and 36 are those at positions 24 up to 35. Their count is \(36 - 23 - 1 = 12\).
The key idea is to unify both ranks to one end and then subtract 1 for the gap, because the two boundary soldiers themselves are not counted as “between”.
Hence the number of soldiers standing between M and N is 12.
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