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        riddles >> medium >> Knights
        
(Message started by: Altamira_64 on Sep 26^th, 2012, 7:18am)

Title: Knights
Post by Altamira_64 on Sep 26^th, 2012, 7:18am

In the attached pdf, can you swap positions of the white with the black knights?
We are not allowed to use any other square except the 10 numbered ones. The knights follow the standard "L" move, like in the chess game. A knight can jump over an existing knight, but can't land on a square where there is already another knight.

Title: Re: Knights
Post by towr on Sep 26^th, 2012, 8:50am

[hide]We have a path 5,7,1,4,10,2,8,9,3 with a split at 4 to 6; thus disentangled, the problem is suddenly a lot easier. And we don't even need 9 and 3.

5,7,1 => 10,2,8
6 => 1
10,2,8 => 7,1,4
4 => 6
7,1 => 10,2
6 => 7
10 => 1
2 => 6[/hide]

Title: Re: Knights
Post by Mercator on Sep 27^th, 2012, 3:52am

Hi towr!
Sorry, I am a novice and don't quite understand your solution :(
Can you please explain in a bit more detailed way?
What do you mean by: "We have a path 5,7,1,4,10,2,8,9,3 with a split at 4 to 6"?
Also, how do you do 5,7,1 => 10,2,8? If not mistaken, you must land on occupated squares, which is not allowed. And so on with all the rest movements.

Many thanks!!!!!

Title: Re: Knights
Post by towr on Sep 27^th, 2012, 9:01am

If you draw lines between the squares where you can reach one from the other with a knights-jump, and then untangle the mess of lines, you'll see that aside from square 6, it's all part of one single path, where you can jump from 5 to 7 to 1 etc.
When you rearrange the squares in that lineup you can consider the problem as one of train-wagons on a rail-system, where you push around (trains of) wagons. So for example I move the "train" on squares 5,7,1 to squares 10,2,8; it's a shorter notation that saying move the knight on square 1 to square 4, then onwards to square 10, then 2 and then 8.

Title: Re: Knights
Post by Altamira_64 on Oct 15^th, 2012, 1:00pm

Now I see :)

And what do you do with square number 6, that is not part of the (initial) path?

Title: Re: Knights
Post by towr on Oct 15^th, 2012, 1:15pm

6 is the sidetrack you use so you can move knights from the back of the 'train' to the front of the 'train'. That's why it features in every second move. It's the crucial bit that actually let's you solve the puzzle, because if it were a single track, then you couldn't change the order. Basically you just move one knight onto the sidetrack, move the train past, move the sidetracked knight to the end of the track, move the train back and repeat.

You can probably construct a puzzle with two or more sidetracks (and more knights, or even a third color) where you also need to use those extra sidetracks. Although it probably doesn't get fundamentally more difficult.

Title: Re: Knights
Post by Altamira_64 on Oct 15^th, 2012, 2:57pm

You are a genius!

Et, comme on dit en Français:
"chapeau, monsieur!"

Title: Re: Knights
Post by alien2 on Nov 8^th, 2012, 1:48pm

Towr. You are a keen-witted earthling and a silver tongued devil. There are quite a few puzzlers, but none of us could solve the beautiful riddle that is you.