There are five different houses A to E in a row. A is to the right of B and E…
2021
There are five different houses A to E in a row. A is to the right of B and E is to the left of C and right of A, B is to the right of D. Which house is in the middle?
- A.
D
- B.
B
- C.
A
- D.
E
Attempted by 12 students.
Show answer & explanation
Correct answer: C
Concept
In a linear arrangement puzzle, each clue fixes a relative order (“left of” / “right of”) between two items. Chain the pairwise relations into a single left-to-right sequence, then read off the required position. For an odd number of items, the middle is the one with an equal count of items on either side.
Application
Translate each clue into an order relation (read “X < Y” as “X is somewhere to the left of Y”):
“A is to the right of B” gives B < A.
“E is to the right of A” gives A < E.
“E is to the left of C” gives E < C.
“B is to the right of D” gives D < B.
Chain them: D < B (from clue 4), B < A (clue 1), A < E (clue 2), E < C (clue 3), giving the single order D < B < A < E < C.
Laid out left to right the row is D, B, A, E, C. With five houses, the third house from either end is the middle, and that house is A.
Cross-check
Count the houses on each side of A: D and B sit to its left (two houses) and E and C sit to its right (two houses). Equal counts on both sides confirm A occupies the central position, and no clue is violated by the order D, B, A, E, C.