Ranking & Seating Arrangement • Topic 1 of 4

Order & Ranking

When a person's rank is given from both ends, Total = left-rank + right-rank − 1 (the person is counted once in each, so subtract the double count). To convert a rank from one end to the other, use right-rank = Total − left-rank + 1.

Why we subtract 1

If a person is 3rd from the left and 4th from the right, counting from both ends counts that person twice. So the total is 3 + 4 − 1 = 6, not 7.

P ←from left: 1 3rd from left · 4th from right from right: 1→
Total = 3 + 4 − 1 = 6 people. P is counted once from each end, so subtract 1.

The three formulas

You wantFormula
Total people (rank given both ends)L + R − 1
Rank from the other endTotal − rank + 1
People strictly between two positions|difference| − 1
Watch the wording. "From the top/left" vs "from the bottom/right" decides which end you count from. "How many are between" excludes both endpoints, so subtract 1.

✅ Solved examples

1. In a row, A is 7th from left and 9th from right. Total people?
7 + 9 − 1 = 15.
2. In a class of 30, B is 12th from the top. Rank from bottom?
30 − 12 + 1 = 19th.
3. C is 5th from left, D is 8th from left. People between them?
|8 − 5| − 1 = 2.
4. In a row of 20, E is 6th from right. Rank from left?
20 − 6 + 1 = 15th.

✏️ Practice — try these, take hints as needed

1. 10th from left, 6th from right. Total?
L+R−1.
—
—
15
2. Class of 40, 15th from top. From bottom?
40−15+1.
—
—
26th
3. 4th and 11th from left — people between?
|11−4|−1.
—
—
6
4. Row of 25, 9th from right — from left?
25−9+1.
—
—
17th
5. 8th from left, 8th from right. Total?
8+8−1.
—
—
15

📝 Topic test — 8 questions

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