Author |
Topic: Knight’s move and original position puzzle (Read 541 times) |
|
K Sengupta
Senior Riddler
Gender: 
Posts: 371
|
 |
Knight’s move and original position puzzle
« on: Jan 16th, 2010, 12:24am » |
 Quote  Modify
|
Using knight’s move in a 3x4 chessboard, can a chess knight situated on any of the 12 squares, visit every other square and land back on its original position?
|
|
 IP Logged |
|
|
|
MathsForFun
Full Member
Posts: 153
|
|
Re: Knight’s move and original position puzzle
« Reply #1 on: Jan 16th, 2010, 12:44am » |
Quote Modify
|
on Jan 16th, 2010, 12:24am, K Sengupta wrote:| Using knight’s move in a 3x4 chessboard, can a chess knight situated on any of the 12 squares, visit every other square and land back on its original position? |
|
This example solution, on board {a..d}{1..3}, entails visiting some squares more than once (which is not forbidden in the question):
a1 c2 a3 b1 c3 d1 b2 d3 c1 b3 d2 b3 (second visit) c1 (second visit) a2
|
|
IP Logged |
Everything is interesting if you look at it closely enough
|
|
|
Obob
Senior Riddler
Gender:
Posts: 489
|
|
Re: Knight’s move and original position puzzle
« Reply #2 on: Jan 16th, 2010, 1:35am » |
Quote Modify
|
Landing on squares more than once is implicitly forbidden.
|
|
IP Logged |
|
|
|
towr
wu::riddles Moderator
Uberpuzzler
Some people are average, some are just mean.
Gender:
Posts: 13730
|
|
Re: Knight’s move and original position puzzle
« Reply #3 on: Jan 16th, 2010, 4:43am » |
Quote Modify
|
If you disentangle the graph, it's very easy to see you can't make a tour when you vist each square only once.
If you don't need to return to the square you start, there are 6 places where you can start such that you can visit the other 11 without visiting a square twice.
|
|
IP Logged |
Wikipedia, Google, Mathworld, Integer sequence DB
|
|
|
|
RIDDLES SITE
WRITE MATH!
Home 
Help 
Search 
Members 
Login 
Register
Reply
Notify of replies
Send Topic
Print