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:
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