Question

Seven people, A, B, L, M, N, S and T, are sitting in a row, facing north(but not necessarily in the same order). No one sits to the right of N. Only three people sit between N and S. Only two people sit between S and T. M sits third to the left of L. A sits to the immediate right of L. How many people sit between B and T?

• A. Two
• B. Three
• C. One
• D. Four

Answer 1

Answer:

B. Three

We’ll solve step by step.

Fix N

“No one sits to the right of N”
Since they face north, everyone is looking north, so right means east side.
So N must be at the extreme right end.

So arrangement ends with:
_ _ N

Positions (left → right): 1 2 3 4 5 6 7
So N = 7

S is 3 people away from N

So difference between N (7) and S is 4 positions apart.

So S = 3
(because only position that keeps 3 people between them is 3)

So:
Position 3 = S

T is 2 people away from S

So T must be 3 positions away from S (since 2 people in between)

From S = 3:
Possible T positions:

• 6 or 0 (invalid)

So T = 6

Now we have:
1 S _ T N
Positions filled: 3=S, 6=T, 7=N

M is third to left of L

So M = L − 3

Try remaining slots: 1,2,4,5

Try L = 5 → M = 2 (valid)

So:
M = 2, L = 5

A is immediate right of L

So A = 6? but 6 already T → not possible
So check again carefully.

We assumed L=5:
Then A would be 6 (occupied)

Try L = 4 → M = 1

So:
M = 1, L = 4
Then A = 5 (immediate right of L)

This works.

Now filled:
1 M, 2 _, 3 S, 4 L, 5 A, 6 T, 7 N

Remaining person B goes to position 2

Final arrangement:
1 M
2 B
3 S
4 L
5 A
6 T
7 N

Count between B and T

B = 2, T = 6
Between them: positions 3, 4, 5 → 3 people

Final Answer: 3 people