Seven boxes—F, I, L, T, E, R and S—are placed one above another, but not…
2026
Seven boxes—F, I, L, T, E, R and S—are placed one above another, but not necessarily in the same order. Only two boxes are below S. Only one box is above I. Exactly one box is between I and F. T is immediately above E. L is somewhere below R. How many boxes are between R and T?
Answer: A. Four — ConceptIn a vertical arrangement of n objects, number the positions from top to bottom. If k objects are below an object, its position from the top is n − k.…
- A.
Four
- B.
One
- C.
Three
- D.
Two
Attempted by 54 students.
Show answer & explanation
Correct answer: A
Concept
In a vertical arrangement of n objects, number the positions from top to bottom. If k objects are below an object, its position from the top is n − k.
“Immediately above” means consecutive positions, while “one box between” means that the position numbers differ by two. Apply the most restrictive clues first and then fill the remaining positions.
Application
There are seven positions. Since only two boxes are below S, S is at position 7 − 2 = 5 from the top.
Since only one box is above I, I is at position 2.
Exactly one box is between I and F, so their position numbers differ by two. From I at position 2, the valid slot for F is position 4.
The unfilled positions are 1, 3, 6 and 7. T is immediately above E, and the only consecutive unfilled pair is 6 and 7. Therefore T is at 6 and E is at 7.
Positions 1 and 3 remain for R and L. Since L is below R, R is at 1 and L is at 3.
Cross-check
Position from top | Box |
|---|---|
1 | R |
2 | I |
3 | L |
4 | F |
5 | S |
6 | T |
7 | E |
The final order from top to bottom is R, I, L, F, S, T, E, which satisfies every clue.
R is at position 1 and T is at position 6. Positions 2, 3, 4 and 5 lie between them and contain I, L, F and S. Thus, four boxes are between R and T.