10 men are fishing in a row boat. The center is empty. The 5 men need to swap places. A man can move to his seat if it is empty or step over one person to an empty seat what are the minimum moves needed for the five men to swap places.
My answer is 25
To determine the minimum number of moves required for the five men to swap places, we need to analyze the scenario and come up with a systematic approach.
Let's first label the initial positions of the men as follows:
1 2 3 4 5 6 7 8 9 10
Initially, the five men who need to swap places are seated as follows:
1 2 3 X X 6 7 8 9 10
To solve this, we can break it down into smaller steps:
Step 1: The first man (1) needs to move to the center (5th seat). He can do this in 2 moves by stepping over the empty seats in between:
1 X 3 X X 6 7 8 9 10
1 X X X 2 6 7 8 9 10
Step 2: The second man (2) needs to move to the seat vacated by the first man (1). Similarly, he can do this in 2 moves by stepping over the empty seats in between:
X X X X 2 6 7 8 9 10
X X X 1 2 6 7 8 9 10
Step 3: The fifth man (6) needs to move to the seat vacated by the second man (2). This can be done in 4 moves:
X X X 1 X 6 7 8 9 10
X X 2 1 X 6 7 8 9 10
X 6 2 1 X X 7 8 9 10
X 6 2 1 10 X 7 8 9 X
Step 4: The fourth man (9) needs to move to the seat vacated by the fifth man (6). This can also be done in 4 moves:
X 6 2 1 X X 7 8 9 X
X 6 2 1 X 9 7 8 X X
X 6 2 1 X 9 7 X X 8
X 6 2 1 X 9 X X X 8
Step 5: The third man (8) needs to move to the seat vacated by the fourth man (9). This can be achieved in 4 moves:
X 6 2 1 X 9 X X X 8
X 6 2 1 8 9 X X X X
X 6 2 1 X 9 X X 8 X
X 6 2 1 X X X X 8 9
Summing up the moves from each step, we get a total of 2 + 2 + 4 + 4 + 4 = 16 moves.
Therefore, the minimum number of moves needed for the five men to swap places is 16, which is fewer than the previously suggested answer of 25.