Discussion
A coin with heads facing up is shown as H and a coin with tails facing up is shown as T.
Six coins are placed in the Starting Arrangement, as shown in the figure below. A “step” is defined as interchanging a pair of adjacent coins without flipping them. The minimum number of steps needed to go from the Starting Arrangement to the Final Arrangement, as shown in the figure, is ________.
| Starting Arrangement | H H H T T T |
| Final Arrangement | T T T H H H |
Answer: C
The minimum number of steps is 9.
Each step swaps two neighbouring coins, so it changes the relative order of exactly one pair of coins. In the starting arrangement H H H T T T every H stands to the left of every T; in the final arrangement T T T H H H every T stands to the left of every H. Each of the 3 × 3 = 9 head-tail pairs has to change its order, and one step can reverse only one pair, so at least 9 steps are needed.
Nine steps are also enough: move the first T leftwards past three H coins (3 steps), then the second T past the three H coins (3 steps), then the third (3 steps).
3 and 6 are too few because they reverse only some of the nine pairs, and 12 is more than the minimum.
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development