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Thinking about a knight's tour made me think of how long it would take other pieces to perform a similar task (touching--or passing over--each square once and once only).
For the Rook's Tour I'm guessing that the "cinnamon roll" approach is the fastest, giving an answer of 15 moves (if I'm counting right).
My question is: is there any way the queen can do it faster than that?
My gut feeling is that the Queen couldn't do it any faster and the method would be the same as used by the Rook.
you can also zigzag to get 15. but i can't see a way for the queen to do it any faster. if you use the diagonals, then it messed up the ranks and files. using the diagonals takes twice as long (or so). using diagonals = a1-a2, b1, c1, a3, etc.
A rook could do every square in 63 moves, not sure how to beat that
Well, to be precise, a "tour" for any piece must be 64 moves, as by definition it entails moving to each square of the board only once and ending upon the beginning square.
Bishops can never do it, and pawns only by promoting to another piece. Of the other pieces, only the Knight presents a difficult problem.
The late George Koltanowski offered as the centerpiece of his standard exhibition a variation on the Knight's tour. He presented at the beginning of his lecture a blank board, allowing the audience to assign any name to each square as they chose. Squares were named after cities, telephone numbers, people, equations, anything suggested. The board, once completed, was put away.
Kolty then conducted whatever lecture or exhibition he was engaged to perform, usually taking an hour or more. At the end he turned his back, and the board with the named squares was returned. The audience named a starting square, either in algebraic notation or using the assigned name. Kolty then conducted a blindfolded Knight's tour, mentioning only the names assigned to the squares, touching each only once. He never failed.
Quite a feat of memory. I've head similar stories where he used telephone numbers or zip codes or something.
Yes, I realize that, that's why I said "similar" (though perhaps I should've said "related," to satisfy the pundit).
I'm thinking it will take the same amount of moves as the rook would take. The cinamon roll pattern for the rook sweeps out a number of squares (including the initial square) with a pattern of 8-7-7-6-6-5-5-4-4-3-3-2-2-1-1 (15 moves). The difference between the queen and the rook is that the queen has the power to move diagonally. I'm assuming that if we move diagonally, then we just count the squares on the diagonal and exclude those that are adjacent to that diagonal as part of the square count. Lets say that we move the queen from a1 to h8. This diagonal has 8 squares (a1, b2, c3, d4, e5, f6, g7, and h8). The queen has some thickness, which means that part of the queen will touch a2, b1, b3, c2, c4, etc...
"Thickness"?...lol Can you do it in under 15 moves anyway? (that's mainly what I'm wondering).
Actually, in addition to the cinnamon roll the rook can also do it (starting from a1) Rh1-h2-a2-a3...etc. Which also takes 15 moves (I wonder if this is all related to the fact that the rook hits the same # of squares no matter where it is on the board).
does thickness have anything to do with fat-bottomed girls and the path of the rockin' world?
Sam Loyd (of course) did some work on this. It seems that to go over every square in 14 moves you have to revisit some squares. http://books.google.com/books?id=47PHOZBdCLYC&pg=PA200&lpg=PA200&dq=sam+loyd+sixty-four+squares&source=bl&ots=2vPpsGfUGk&sig=Q-YSQ6S1eIzDnZqGfY9fj-zdjA4&hl=en&ei=5qTITPW4Joa0lQeq48znAQ&sa=X&oi=book_result&ct=result&resnum=6&ved=0CCcQ6AEwBQ#v=onepage&q=sam%20loyd%20sixty-four%20squares&f=false
The actual Knights tour was landing on each square once and returning to the original starting square. That would be 64. If the condition was also passing over the the Knights tour would not work.
In the Rook or Queens tour just landing and passing over a square is being counted. It is quite a difference. But a good exercise.
This one's called the Turks Knights tour. I made it easy to follow using colors.
Permission to copy it for any reason.
You will never satisfy the pundit. Satisfied pundits have their pundit licenses immediately revoked by a Panel of Experts.
An actual pundit:
The scarf says: "It's not hot! I reject all meteorological arguments today."
Well, since the guy's from India, I'd say it's probably gotten down to 110 so he has to bundle up a bit.
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