13442 Players currently online!
Man vs. Machine - good luck!
Turn-based games at any time!
Vote for the best move to win!
Do you have what it takes?
Sharpen your tactical vision!
Get advice and game insights!
Learn from top players & pros!
View millions of master games!
Your virtual chess coach!
Perfect your opening moves!
Test your skills vs. computer!
Find the right private coach!
Can you solve it each day?
Bring it all together!
Beginners, start here!
Make friends & play team games!
News from the world of chess!
Search all Chess.com members!
Find local clubs & events!
Who's the best of your friends?
Read what members are saying!
Solving the "Knight's Tour" math problem involves moving the knight about the chessboard such that each square is visited exactly once.
Visualizing the chessboard as 4 quadrants, memorizing a small group of patterns within each quadrant, and following a few simple principles while calculating the knight moves will allow you to find a solution to this fun mathematical problem.
It's an intuitive puzzle to challenge a friend, math teacher, or even a math classroom with.
I've provided a solution to this math problem in this video: http://www.youtube.com/watch?v=9fSFC00ZKPg
I solved this a while ago too, even for bigger boards:
In a 15x15 board:
Thanks, not going to bed until I do this.
Thanks Gerry! Awesome.
(Disclaimer: did start trying before my first message).
Sounds fun, don't know if I have time.
Another idea is when breaking the board down into quadrants, is to also devise patterns based on easily recognizable shapes and then determine a pattern based on those shapes.
Here is an example:
You can envision the Knights making a diamond-shaped pattern by the moves from a8-b6-d5-c7 and a square being made from the moves a6-b8-d7-c5. Now, if these could be repeated in a particular way, you could travel in all four quadrants and reach all 64 squares from starting on a8 and ending on h6 having to familiarize yourself with only four moves at a time.
Next think of the upper left quadrant as 1, the lower left 2, lower right 3, and upper right as 4 and the most complex of these patterns is the formation of Diamond, Square, Square, Diamond followed by Square, Diamond, Diamond, Square.
Putting the two concepts together we get:
D1, S1, S2, D2, S3, D4, D3, S3, D2, S2, S1, D1, S4, D3, D4, S4.
Here is the pattern over the board:
This is the most complex of the patterns I have found aside from the Euler's Square. I was able to work out 3 other patterns as well, those being:
See if you can find the patterns of the Knights moves into the quadrants in these.
Nice way to understand it, thanks CN :-)
Magnus Carlsen blitz (Norway Chess 2013) video
by Reb a few minutes ago
Computer Analysis says 1...c5 is an Inaccuracy ???
by uhohspaghettio a few minutes ago
Quickest game #5
by andressimancasmateus a few minutes ago
Choose: (1) ....0-0 or (2) ...Bxg2
by yeres30 3 minutes ago
by uhohspaghettio 3 minutes ago
5/23/2013 - The Long Road Home
by joaolima39 4 minutes ago
by Master_Valek 5 minutes ago
FM Borislav Ivanov Disqualified
by mladigaleb 6 minutes ago
Concerned about trolling, again
by Master_Valek 13 minutes ago
Piece set recognition
by CLINTEASTW00D 13 minutes ago
Why Join | Chess Topics |
Help & Support |
© 2013 Chess.com