Logical Puzzles
Hard
4 min
Four people A, B, C and D must sit in four consecutive seats. A cannot sit next to B. C must sit immediately to the left of D. How many valid arrangements are possible?
Hint
Treat C-D as one block.
Answer
4 arrangements.
Explanation
The block CD can occupy positions 1-2, 2-3 or 3-4. Checking the remaining placements while ensuring A and B are not adjacent gives four valid arrangements.
Step-by-Step Solution
Possible valid arrangements:
C-D-A-B is invalid because A and B are adjacent.
A-B-C-D is invalid.
B-A-C-D is valid.
C-D-B-A is valid.
A-C-D-B is valid.
B-C-D-A is valid.
Therefore there are 4 valid arrangements.
C-D-A-B is invalid because A and B are adjacent.
A-B-C-D is invalid.
B-A-C-D is valid.
C-D-B-A is valid.
A-C-D-B is valid.
B-C-D-A is valid.
Therefore there are 4 valid arrangements.