# Four Knight Tours

greenpawn34
Posers and Puzzles 29 Jun '08 19:09
1. 29 Jun '08 19:09
This just popped into my head whilst playing over a game
30 minutes ago.

White Knights on a1 and h8
Black Knights on h1 and a8

The a1 Knight Knight moves first, then a8, h8 and h1.

Same rules as standard a Knight's tour
No Knight can land on a square that has already been visited by a Knight.

All squares must be covered and the Knights must end up
on d4,e4,d5 and e5.

I've not tried it yet.
But I have a feeling it can be done and it is most likely easy.
I've been doing it in my head and it seems to just flow along.

But I will try it later on tonight to be sure.

The trick to doing a normal single Knight's tour is to always take a
square furthest from the centre and you will eventually work your
way inwards.
2. 29 Jun '08 19:39
I've never tried a normal "Knight's tour", is it worth your time? Also, while you are at it, could you explain how exactly a normal Knight tour works? (I know a Knight has to visit all squares but no more than that)
3. 29 Jun '08 22:19
The Knight starts off on say h1 and you visit each of the 64 squares
only once. You usually finish on a central square d4,d5,e4,e5.

There are many solutions. There are free wee programs on various
sites where you can try it on a computer. The comp shades in
each square and keeps you right. Much easier to use.

I've seen a guy who did it blindfold and you could start the Knight on
any square of your choosing. I do not think there is a bogey
square from which it cannot be done.
4. 30 Jun '08 06:432 edits
Greenpawn, I pwn the guy you met. I can do this feat blindfold, starting from any specified square and ending on any specified square (of the opposite colour). If you want to try me, name two squares and I'll give the answer for those two (I don't think there's a computer program that does this, and you'll have to trust that I'm blindfold ðŸ˜‰). For the record, yeah, I'm 17 and have few friends. This makes me feel big.

As for the puzzle, yes it's easy, as there are circular knights tours (as in, tours that end up back at the start). Thus you just complete that circle for the two knights. You could complete a knights tour with 63 knights on the board this way; effectively you'd just be doing a knights tour, backwards, with the gap.
5. 30 Jun '08 11:05
I believe you.
Though it was not you. This guy was bald and was on stage.

There is a program that will do one tour. It's in it's memory
so of course it just trots it out.

Not seen one that can do it from any square and finish on any square.
You do this blindfold! I believe you.

How would you like demonstrate this skill. And it is a skill, at a
congress in August/October. There is always a gap inbetween
the tournament ending and the prize giving.
I've been asked to do a demo for 30 minutes but would gladly
step down so we can witness this.

I'm doing it for a few pints and a packet of fags. (cigarettes).

If you do it I'll get them to pay...say £20.00 and (free entry
to the tournament - most likely Dundee.)

Or there is a massive tournament coming up in Glasgow at
the Kelvingrove Museum. Do it there infornt of 100's of people.
and you will end on Chandler Cornered, interviwed by Radio Clyde
and have you picture in the Scottish Chess Magazine.

You will have more than just a few friends - you will be famous.
What do say?

I am serious by the way. PM me.
6. 30 Jun '08 14:54
I have been trying this on an online application (just search for Knight's Tour and it will come up) after trying it on a normal board already. I can't get it right. Reminds me of the Troyis game.

http://www.troyis.com/
7. 01 Jul '08 15:30
Originally posted by greenpawn34
The Knight starts off on say h1 and you visit each of the 64 squares
only once. You usually finish on a central square d4,d5,e4,e5.

There are many solutions. There are free wee programs on various
sites where you can try it on a computer. The comp shades in
each square and keeps you right. Much easier to use.

I've seen a guy who did it blindfold ...[text shortened]... square of your choosing. I do not think there is a bogey
square from which it cannot be done.
Actually, I do recall a circular Knight's Tour is indeed very possible. A circular Knight's Tour is a Knight's Tour where the starting square and the ending square are a knight's move apart, which has the same effect as splicing two ends of the same string together.

In other words, you can move from the last square to the first or visa versa, because the entire tour is a loop rather than merely a path.

The result is that you can start from anywhere in that tour, and since it covers all 64 squares, you can thus start a tour from any square (or in either direction)
8. 01 Jul '08 16:291 edit
Heh, thanks for the offer greenpawn but I'm really not so confident as to do it in front of that many people, and I'm not sure any reasonable amount of money would cover the flights up there and back (my parents said they would not be happy driving). If you're ever in the west midlands area on a Thursday though, message me and I'll give you directions to the chess club I attend for a little demo ðŸ™‚

Actually, it's very likely I'll be going up to Edinburgh university in a year and a bit, so if that happens, you could give me directions to your place and I'll show you then.

edit: oh, and if you're a bit impatient, message me and I'll give you a series of messages explaining my method.
9. 01 Jul '08 18:59
Sandy Bells is a pub near the University - It has 3 teams in
the Edinburgh League and hopefully next season there will
be an all girls team. Bells Girls. (or Bells Belles).

You will like Bells - no blaring hip hop music, no plastic furniture and
is not a tourist trap. Within two visits the bar staff will know your name
and what you drink. Live music every night, 4 chess sets and clocks
behind the bar. It's often freqiented by some very strong players...
...and me.

A while back one of our players played 6 blindfold games there winning
all six in under 2 hours. A blindfold knights tour demo would be a treat.

Post your technique here - I'm sure the other guys on here will
be interested.
10. 01 Jul '08 20:10
K. A lot of this is someone else's method but I cannot remember the original theorist:

1) Split the board up into 4 quarters
2) We have four pattens, in the bottom left quarter, the patterns are this:
Left diamond - A4, B2, C3, D1
Right diamond - A1, B3, C2, D4
Left square - A2, B4, C1, D3
Right square - A3, B1, C4, D2

Identify which of these patterns the start and end squares lie in.

3) If they lie in opposite shapes (square/diamond) then you complete all the squares that are within the same shape as your starting square. I.E. if you started on C3 and you're wanting to end on G8, the first thing you would do is colour the following squares:
C3, D1, B2, A4, B6, A8, C7, D5, F6, E8, G7, H5, G3, H1, F2, E4....
4) Next, you fill in all the squares that lie within the opposite shape (square/diamond) that isn't the same as your ending squares shape. And then you repeat this stage, and then once more, and you've done it.
5) If the starting square and ending square are the same shape but differing directions, then you complete stage 3 as normal, but when you get to your third shape, you will have to go to that of your ending square, and so you want to complete that shape for everything but the ending square, then go to the last shape you haven't completed, and finish.
6) If the starting and ending square are the same shape and same direction then you basically do step five, but isolate the ending square quicker.

As for doing this blindfold... well, just practice your visualisation really.
11. 01 Jul '08 21:20
Cheers - I'm going to have a shot at this - thanks.
12. 02 Jul '08 14:55
Chance has it that today in a Dutch magazine an example Knight's tour was published. The Dutch term apparently is Knight's Pirouette. Something about a special magical square is mentioned - add all numbers of a file/rank, the outcome is always 260 [(1+64) x 8/2]. Another characteristic is that this an 'closed' Knight's tour; from square 64 you can immediately hop back to square 1 (term is 'buler' according to the magazine).

50-11-24-63-14-37-26-35
23-62-51-12-25-34-15-38
10-49-64-21-40-13-36-27
61-22-09-52-33-28-39-16
48-07-60-01-20-41-54-29
59-04-45-08-53-32-17-42
06-47-02-57-44-19-30-55
03-58-05-46-31-56-43-18

Quite fascinating, although I must admit that I have no idea what's going on.
13. 02 Jul '08 18:15
Thanks for that - I can see a small space filler coming
up in future column. I have acouple of regulars who are
avid Knight's tour fans.

One sent me a lengthy article about prime numbers and
Knight tours. Baffled me completely.
14. 02 Jul '08 18:46
Oh, in my hastiness I forgot to credit the knight's pirouette magic square source: J. Gyzicki: The World of Chess. (and the article where I read about it is in 'Schaakmagazine' of June 2008).
15. eldragonfly
leperchaun messiah
02 Jul '08 20:58
Originally posted by doodinthemood
Greenpawn, I pwn the guy you met. I can do this feat blindfold, starting from any specified square and ending on any specified square (of the opposite colour). If you want to try me, name two squares and I'll give the answer for those two (I don't think there's a computer program that does this, and you'll have to trust that I'm blindfold ðŸ˜‰). For the ...[text shortened]... board this way; effectively you'd just be doing a knights tour, backwards, with the gap.
You're a liar.