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# Touring the chessboard with a single die

9 replies to this topic

### #1 bonanova

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Posted 08 June 2012 - 04:50 AM

I read this one a while back and found it challenging.

Place a single die on QR8 of a chessboard, or a smaller 8x8 grid of squares.
The die "moves" from square to square by tipping on its side in a N, E, S or W direction,
[thus] making a 1/4 turn each time it moves to a new square.

The object is for the die to move to each of the squares, only once, and finish on KR8.
That is to tour the board beginning on the NW corner and end on the NE corner.

The final constraint is that the 1-spot must be up on the beginning and ending squares,
but on none of the intervening squares.

To describe the tour, number the board left to right so that the top row (8th rank)
Is 1 2 3 4 5 6 7 8 and the bottom row (1st rank) is 57 58 59 60 61 62 63 64.

Again, begin on square 1, and end on square 8.
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Vidi vici veni.

### #2 CaptainEd

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Posted 08 June 2012 - 05:06 AM

I understand the die tipping over onto an adjacent face. Is that the "1/4 turn" you mention, or is there an additional quarter turn (ie, on some other axis)
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### #3 bonanova

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Posted 08 June 2012 - 05:09 AM

I understand the die tipping over onto an adjacent face. Is that the "1/4 turn" you mention, or is there an additional quarter turn (ie, on some other axis)

That is the only turn. OP edited to clarify that point.
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Vidi vici veni.

### #4 phil1882

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Posted 08 June 2012 - 02:31 PM

Spoiler for got it on my first try

Edited by phil1882, 08 June 2012 - 02:35 PM.

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### #5 EventHorizon

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Posted 08 June 2012 - 11:14 PM

Spoiler for got it on my first try

At position 5 the 1 is on top of the die again breaking that constraint. Unless, that is, if I'm misreading the constraints.
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### #6 phil1882

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Posted 09 June 2012 - 02:03 AM

ah your right i feel silly now.
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### #7 EventHorizon

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Posted 09 June 2012 - 01:20 PM

Spoiler for Solution

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### #8 superprismatic

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Posted 09 June 2012 - 08:49 PM

Spoiler for Solution

Very nice, EventHorizon! I was just about to write a backtracking program when I saw that you beat me to it.
I was going to have mine check to see if there were any other ending grid squares besides square 8.
I never programmed in C++, so I can't decipher your code. I ran it and it took about 3 minutes on my
machine to come up with the solution you posted. Would it be easy to modify your code so that it looks
for endpoints (with the 1 up) other than square 8? Congrats!
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### #9 EventHorizon

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Posted 10 June 2012 - 08:02 AM

Very nice, EventHorizon! I was just about to write a backtracking program when I saw that you beat me to it.
I was going to have mine check to see if there were any other ending grid squares besides square 8.
I never programmed in C++, so I can't decipher your code. I ran it and it took about 3 minutes on my
machine to come up with the solution you posted. Would it be easy to modify your code so that it looks
for endpoints (with the 1 up) other than square 8? Congrats!

Yeah, it would be easy. So easy in fact... that here it is
Spoiler for Changes

Spoiler for The new code

Spoiler for Output

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### #10 EventHorizon

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Posted 12 June 2012 - 03:43 PM

Spoiler for First, more code...

Spoiler for Pictures my code drew...

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