Order & Ranking
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How ranking questions work
Rank from the other end
p' = n + 1 - p
n = total people, p = rank from one end.
Total from two ranks
n = a + b - 1
The same person is a-th from one end and b-th from the other end.
Between count (same end)
\text{between} = |a - b| - 1
Both ranks are from the same end.
Ahead and behind
\text{ahead} = r - 1,\quad \text{behind} = n - r
r = the person's rank from the front.
Ranks and positions
Rank from the other end
p' = n + 1 - p
n = class size or row size.
Total from two ranks
n = a + b - 1
The same person, ranked from both ends.
People joining or leaving ahead
r_{\text{new}} = r_{\text{old}} \pm k
Plus for k joiners ahead. Minus for k leavers who were ahead.
People between two positions
Between, same end
\text{between} = |a - b| - 1
Both ranks are counted from the same end.
Between, opposite ends
\text{between} = n - a - b
n = total people, a and b = ranks from opposite ends.
Middle person
m = \dfrac{a + b}{2}
a and b from the same end. The result must be a whole number.
Rank from the gap
b = a + k + 1
k people are between a and b, counted from the same end.