Closed tour of a Knight
When a Knight moves in chess, it can move to a square that is away two squares horizontally and one square vertically,or two squares vertically and one square horizontally.A closed tour for a Knight is a sequence of moves,which have the Knight start and end in the same square and visit each other square exactly once.On a $4 \times 3$ board,is there a possible closed tour for a Knight?
"Questions we can't answer are far better than answers we can't question"
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- Posts:1007
- Joined:Sat Dec 09, 2017 1:32 pm
Re: Closed tour of a Knight
Hint
Answer
$4×3$ Chess Board
Answer
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- Posts:1007
- Joined:Sat Dec 09, 2017 1:32 pm
Re: Closed tour of a Knight
Ignore the above solution.
Correct Solution
Let the tour is possible.
Total move $=12-1=11$
In every move it alters the color of the square.If the starting square is black,the ending square is not black.(Imagine it as a traditional chess board)
But,move number is odd.
A contradiction.
So,we are done.It is not possible.
Correct Solution
Let the tour is possible.
Total move $=12-1=11$
In every move it alters the color of the square.If the starting square is black,the ending square is not black.(Imagine it as a traditional chess board)
But,move number is odd.
A contradiction.
So,we are done.It is not possible.