## Square Sudoku

For fans of Killer Sudoku, Samurai Sudoku and other variants

### Square Sudoku

Fill in the grid so that every row and every column contains the digits 1 through 9. The points mark corners of squares. These squares have the size 2x2 or 3x3. No pair of squares can touch each other on corners or borders, but they can overlap similar to the picture with the blue squares. Number in squares must be different.

There is only one solution. You can find it by logic.

Last edited by Pyrrhon on Thu Nov 16, 2006 7:44 am, edited 1 time in total.
Pyrrhon

Posts: 240
Joined: 26 April 2006

I assume another rule is, only one corner of each box is shown, so that there are 9 boxes in this particular puzzle.

Also, there seems to be a misprint. That dot on the right edge belongs at the lower right corner of r5c9, right?

Bill Smythe
Smythe Dakota

Posts: 564
Joined: 11 February 2006

Yes, there is only one point per square (9 squares at all) The misprint is corrected.
Pyrrhon

Posts: 240
Joined: 26 April 2006

Are we assured the solution is unique, not only for the placement of the digits, but also for the location and size of the boxes?

For example, if it were to turn out that the box whose lower left corner is r6c3 could be either 2x2 or 3x3, would that be considered a dual solution which would "cook" the puzzle?

Bill Smythe
Smythe Dakota

Posts: 564
Joined: 11 February 2006

There is only one position of the squares possible. But uniqueness techniques are not necessary to solve the puzzle.

Pyrrhon
Pyrrhon

Posts: 240
Joined: 26 April 2006

Here is the solution.

I solved it with an assumption that there are 4 2x2 boxes and 5 3x3 boxes... Without this assumption there could be different solutions with, say 7 2x2 boxes and 2 3x3 boxes... So I think it'd be nice if Uwe would specify the number of 3x3 boxes in the puzzle description...

Hint: a grouped turbot fish on 7 helps to crack it... Also keep an eye on implied 3x3 boxes with established boxes...
udosuk

Posts: 2698
Joined: 17 July 2005

udosuk wrote:Without this assumption there could be different solutions with, say 7 2x2 boxes and 2 3x3 boxes...

You're right, there are then multiple solutions
Here is such a possible solution

Another hint:
After, finding the squares in R678C123 & R678C789, using LoL, one can deduce that R678C456 also forms a 3x3 square with each digit once
Jean-Christophe

Posts: 149
Joined: 22 January 2006

Sorry, there was some knot in my brain. I will come with a improved example.

Pyrrhon
Pyrrhon

Posts: 240
Joined: 26 April 2006

Here is now my improved version of the puzzle. The points are the same, the numbers are changed.

Pyrrhon

Posts: 240
Joined: 26 April 2006

Thanks for the correction. Now, if you wish, you can delete your last post (following this one), then I can delete this one. (The system won't let me delete my post right now because it's not the last one.)

Bill Smythe
Last edited by Smythe Dakota on Sun Nov 19, 2006 7:01 pm, edited 1 time in total.
Smythe Dakota

Posts: 564
Joined: 11 February 2006

They must be on the same place. I've correct it.

Pyrrhon
Pyrrhon

Posts: 240
Joined: 26 April 2006

For the correct version, it's quite easy to establish 6 boxes, and then some fishy moves will solve all 81 cells, and then you can determine the final 3 boxes...

Solution:

976583124
419238576
521647938
754961283
238754691
682319457
147825369
395476812
863192745

Solution pic

For the incorrect version, you can determine all 9 boxes quite easily early, but then you can only progress to this state, where a total of 4 different solutions are possible:

976485123
419538276
521647938
754961382
238754691
682319457
147823569
395276814
863192745

976583124
419238576
521647938
754961283
238754691
682319457
147825369
395476812
863192745

976485123
419532876
561247938
754961382
238754691
682319457
147823569
395678214
823196745

976485123
419538276
561247938
754961382
238754691
682319457
147823569
395672814
823196745

Note to self: next time Uwe release a puzzle, wait at least one month for others to report any typos etc, because a lot of time can be wasted on an invalid puzzle!
udosuk

Posts: 2698
Joined: 17 July 2005

udosuk wrote:For the incorrect version, you can determine all 9 boxes quite easily early, but then you can only progress to this state, where a total of 4 different solutions are possible:

Note to self: next time Uwe release a puzzle, wait at least one month for others to report any typos etc, because a lot of time can be wasted on an invalid puzzle!

Hey, you forgot the box with corner at R6CA
Jean-Christophe

Posts: 149
Joined: 22 January 2006

Jean-Christophe wrote:Hey, you forgot the box with corner at R6CA

JC, I was talking about this puzzle, posted earlier by Uwe, where there is no "corner at r6cA"...

udosuk

Posts: 2698
Joined: 17 July 2005