21043 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?
Backgammon, Yatzy, and more!
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 :-)
Tired of sandbagging players
by weakatbullet a few minutes ago
Help with filtering out just moves in .pgn
by Martin_Stahl a few minutes ago
Who "decides" which opening to use?
by Nevada2012 2 minutes ago
Falling asleep to chess lectures.
by chessspy1 4 minutes ago
Thoughts on people who illegally download chess books?
by gromius 5 minutes ago
Proverbial "stalemate" ?
by aidan0816 6 minutes ago
by super-bird 8 minutes ago
Sicilian Defense Dragon Variation
by Sid31 13 minutes ago
Of course you owe a rematch
by Lasker1900 19 minutes ago
by Lasker1900 20 minutes ago
Why Join | Chess Topics |
Help & Support |
© 2016 Chess.com
• Chess - English
Try the new Chess.com!
We are working hard to make Chess.com available in over 70 languages. Check back over the year as we develop the technology to add more, and we will try our best to notify you when your language is ready for translating!