## 3 chess-related Sudoku challenges

For fans of Killer Sudoku, Samurai Sudoku and other variants

### 3 chess-related Sudoku challenges

Challenge 1 (difficulty: easy)

These 2 Sudoku grid shares one chess-related special property. Can you identify it?
Code: Select all
`426759183318642975597831264183426759975318642264597831759183426642975318831264597657324981432198765819576243981657324765432198243819576324981657198765432576243819`

Challenge 2 (difficulty: medium)

Change 6 cells in each of the 2 grids in Challenge 1 to obtain 2 other grids which have the same chess-related property.

Challenge 3 (difficulty: hard)

There is a 5th grid which also has the same chess-related property. It is obtainable by changing 65 cells in either one of the 2 grids in Challenge 1. Can you find it?
udosuk

Posts: 2698
Joined: 17 July 2005

As I'm not good with these chess pieces (especially the leapers ). I focused on the ones I know & still can't see it

Maybe I'm missing the rules here

I found a link somewhere to these chess moves but lost it . Will try again

tarek

tarek

Posts: 3759
Joined: 05 January 2006

tarek wrote:As I'm not good with these chess pieces (especially the leapers ). I focused on the ones I know & still can't see it

Maybe I'm missing the rules here

You must have known this chess piece for life. Challenge 1 isn't meant to be hard. The piece is a well known piece and the rule is a simple rule. This rule can be abbreviated in 3 letters and has been mentioned before.

It's Challenge 2 which is interesting. Changing only 6 cells to preserve the property. These are the only ways to alter these 2 grids with fewer than 54 cells changed (i.e. all other solution grids with this property are at least 54 cells different to these grids).
udosuk

Posts: 2698
Joined: 17 July 2005

udosuk,

Are we back on the 8 Queens again, in some way? The other main chess-related thing tends to be the Knights Tour and its variations
Bigtone53

Posts: 413
Joined: 19 September 2005

Bigtone53 wrote:Are we back on the 8 Queens again, in some way? The other main chess-related thing tends to be the Knights Tour and its variations

Nope, nothing to do with Queens. It's the other piece which you have mentioned, but nothing to do with "Tour" or "Circuit" etc. It's just a very simple and well known Sudoku Variant, even mentioned in some recent threads in this section.

I'm quite surprised nobody worked out Challenge 1 yet. Just for another hint, if you take 1 of the 2 grids in Challenge 1, transposing it (i.e. reflecting about the main diagonal), and then put it side by with the other grid, what do you notice?
udosuk

Posts: 2698
Joined: 17 July 2005

I can see that the 1s 4s and 7s in the first grid and the 3s 6s and 9s in the second grid are knight's moves apart (assuming top-to bottom and side-to-side carryover), but eerrrr
Bigtone53

Posts: 413
Joined: 19 September 2005

Bigtone

As a clue note I claim "invention/discovery" of it!!! (In the English Sudoku world of course - we can never be sure what has already been done in Japan.)

However I'm getting nowhere with Matt's challanges.

Maurice
HATMAN

Posts: 276
Joined: 25 February 2006
Location: Saudi Arabia

Please just try to fill in the follow blanks (one ? = one letter) to get the answer for Challenge 1:

For the answer of Challenge 1 I wrote:The common property of the 2 grids is that within each grid, all cells a ??????'s move apart must be ???-??????????? (i.e. the numerical difference must not be ???).

Maurice (HATMAN) is correct that he introduced this property to us in this very forum.

For Challenge 2 - coloin (and other deadly pattern experts) should be the best equipped to crack it as it requires spotting 6 cells in the solution grid which can be permuted so that both the Sudoku rules and the special property is not violated. But if one is equipped with a software like JSudoku and play around with the grids (e.g. clearing a whole region of cell) and then use the "recursively solve" feature it's not impossible to work out the answers.
udosuk

Posts: 2698
Joined: 17 July 2005

OK, I have found HATMAN's chain and can see what is going on.
Bigtone53

Posts: 413
Joined: 19 September 2005

I must confess that I couldn't visulaize it properly....

I'm not sure how easy it is for other people .... but you have to go through most combinations to get it.

It looks like a knight non-consecutive for challenge 1 ....

I think the best thing out of this challengew was to learn about fairy chess pieces & history of chess

tarek

tarek

Posts: 3759
Joined: 05 January 2006

tarek wrote:I think the best thing out of this challengew was to learn about fairy chess pieces & history of chess

In that case you're equipped to tackle this challenge:

http://www.djape.net/sudoku/forum/viewtopic.php?t=1303

udosuk

Posts: 2698
Joined: 17 July 2005

too much chess for one day .....

I'm currently working on developing overlapping puzzle generator. That is occupying most of my free time thinking

tarek

Posts: 3759
Joined: 05 January 2006

As most of us should have already known the answer for Challenge 1 is NNC (kNight Non-Consecutiveness).

Now for Challenge 2, how do you change only 6 cells and preserve this property? Here are some hints:

Triple click to read the hints I wrote:For the 1st grid, the 6 cells are all within the 3 leftmost columns involving only 2 numbers.

For the 2nd grid, the 6 cells are all within the 3 rightmost columns involving only 3 numbers.

udosuk

Posts: 2698
Joined: 17 July 2005

### Re: 3 chess-related Sudoku challenges

For Challenge 2 I'll show you which 6 cells to change. All you need to do is to fill in the new numbers:

Triple click to see the grids I wrote:426759183
``8642975
597831264
`8`426759
975318642
264597831
759183426
642975318
8``264597

657324`8`
432198765
819576243
981657324
765432`9`
243819576
324981657
198765432
576243`1`
udosuk

Posts: 2698
Joined: 17 July 2005