Each trick says when to use it, why it works and when it fails. Formula tricks are checked by code over their whole range.हर ट्रिक बताती है कि उसे कब इस्तेमाल करें, वह क्यों काम करती है और कब नहीं। सूत्र वाली ट्रिक्स को कोड से उनकी पूरी रेंज पर जाँचा गया है।
Formulaसूत्रRarely taughtकम सिखाई जाने वाली✓ Checked on 71,978 cases✓ 71,978 मामलों पर जाँची गई
Two positions from opposite ends: the crossing check
Use it when:कब इस्तेमाल करें: A is p-th from the left and B is q-th from the right in a row of N. How many sit between them?
If p + q ≤ N: between = N − p − q.
If p + q > N (they have crossed): between = p + q − N − 2.
Exampleउदाहरण
N = 40, A 12th from left, B 15th from right
→ 27 ≤ 40 → 40 − 27 = 13 between
Why it works, and when it failsयह क्यों काम करती है, और कब नहीं
Why:क्यों: From the left, B is at N − q + 1. The people strictly between two seats x and y number |x − y| − 1, which gives both formulas.
Limits:सीमाएँ: Assumes A and B are different people and both positions fit inside the row.
Exam strategyपरीक्षा रणनीति
Fixed clues first, negative clues last
Use it when:कब इस्तेमाल करें: Any seating or ordering puzzle with five or more people.
Number the seats. Place clues that fix a seat (ends, “third from the left”).
Attach neighbour and gap clues to people already placed, branching into two rows only when a clue allows two places.
Use “is not next to” and “does not sit at an end” clues last, to remove branches.
Exampleउदाहरण
A sits at an end; B is immediately right of A; C is third from the left.
→ C fixes seat 3; A must be at the left end (seat 1) for B to fit at seat 2.
Why it works, and when it failsयह क्यों काम करती है, और कब नहीं
Why:क्यों: Fixed clues shrink the possibilities the most, so placing them first keeps the number of rows you must track small.
Limits:सीमाएँ: Some puzzles have no fixed clue; then start from the person mentioned in the most clues.
Solved examplesहल किए गए उदाहरण
Answers and full solutions are shown. Hide them to test yourself first.उत्तर और पूरे हल दिखाए गए हैं। पहले खुद को परखने के लिए इन्हें छिपाइए।
Example 1उदाहरण 1 · Ranking and order (position in a row) · Easyआसान
In a queue at the ticket counter, Priya is 30th from the left and 7th from the right. How many people are there in total?
29
32
36
45
Answer:उत्तर:36
Total = 30 + 7 − 1 = 36.
Example 2उदाहरण 2 · Ranking and order (position in a row) · Mediumमध्यम
In a row of students at morning assembly of 52 people, Ayaan is 5th from the left and Fatima is 6th from the right. How many people are between Ayaan and Fatima?
33
41
45
49
Answer:उत्तर:41
Ayaan and everyone to the left: 5. Fatima and everyone to the right: 6.
Between = 52 − 5 − 6 = 41.
Example 3उदाहरण 3 · Ranking and order (position in a row) · Hardकठिन
In a row of girls and boys, Fatima is 8th from the left and Arjun is 13th from the right. When they interchange their positions, Fatima becomes 11th from the left. How many people are in the row?
17
21
23
25
Answer:उत्तर:23
Fatima takes Arjun's place: 11th from left, 13th from right.
Total = 11 + 13 − 1 = 23.
Example 4उदाहरण 4 · Ranking and order (position in a row) · Mediumमध्यम
There are 59 people in a line of cricket fans outside the stadium. Vihaan is 31st from the left. What is Vihaan's position from the right?
22
23
26
29
Answer:उत्तर:29
People to the right = 59 − 31 = 28.
Position from right = 28 + 1 = 29.
Example 5उदाहरण 5 · Ranking and order (position in a row) · Mediumमध्यम
There are 37 people in a class ranked by marks. Diya is 25th from the left. What is Diya's position from the right?
10
12
13
16
Answer:उत्तर:13
People to the right = 37 − 25 = 12.
Position from right = 12 + 1 = 13.
Example 6उदाहरण 6 · Ranking and order (position in a row) · Mediumमध्यम
In a row of students at morning assembly, Meera is 9th from the left and 16th from the right. How many people are there in total?
19
22
24
29
Answer:उत्तर:24
Total = 9 + 16 − 1 = 24.
Common mistakesआम गलतियाँ
Forgetting to subtract 1 for the person counted twice.
Mixing positions from different ends.
Frequently asked questionsअक्सर पूछे जाने वाले प्रश्न
How do I find the total number of people in a row?
Add the positions from both ends and subtract 1.
How many people are between two persons?
Use positions from the same end: difference − 1.
What if the two positions overlap?
If A’s position from the left plus B’s position from the right is more than the total, they have crossed: people between = that sum − total − 2.