## 123 sudoku

For fans of Killer Sudoku, Samurai Sudoku and other variants

### 123 sudoku

There seems to be only easy sudoku with many givens in this variant. Here is an example:

Fill in the grid so that every row, every column, and every 3x3 box contains the digits 1 through 3. Each row, column, and box contains three 1's, three 2's and three 3's.

You can solve it by logic.

Last edited by Pyrrhon on Fri Jul 28, 2006 3:16 pm, edited 2 times in total.
Pyrrhon

Posts: 240
Joined: 26 April 2006

There seem to be at least three solutions -- two with a 2 in r8c7 (in this case the six cells at r3c5, r3c6, r4c1, r4c5, r5c1, r5c6 can be filled in either of two ways), and one with a 1 in r8c7 and a 2 in r9c7. There may be additional solutions with a 1 in r8c7 and a 1 in r9c7.

Bill Smythe
Smythe Dakota

Posts: 564
Joined: 11 February 2006

Thank you for your hint. I must had made a mistake in painting the picture. I can remember the methods used to solve it but I can't find my original grid. I will give another sudoku of this variants some days later.

Pyrrhon
Pyrrhon

Posts: 240
Joined: 26 April 2006

This is about the 123a puzzle from Pyrrhon's homepage... I'm up to the following stage:

... and don't know how to continue... Any help? Thanks!
udosuk

Posts: 2698
Joined: 17 July 2005

Well, I can see one thing. There must be 3's in two of r5c5, r5c7, r5c9. But the latter two cannot both be 3's, so r5c5 must be a 3.

Bill Smythe
Smythe Dakota

Posts: 564
Joined: 11 February 2006

Good spotting... Thanks Bill!
udosuk

Posts: 2698
Joined: 17 July 2005

You're welcome. From this point on, though, I had to use trial and error (something I'm never opposed to when solving tough puzzles). If you find something better, please let me know.

Since there must be a 3 in either r5c7 or r5c9, there cannot be a 3 in either r6c7 or r6c9, which means there must be a 3 in either r6c4 or r6c5. One of these leads (eventually) to a contradiction, the other to a solution.

Bill Smythe
Smythe Dakota

Posts: 564
Joined: 11 February 2006

You don't need T&E... There is an x-wing on 3s in r26c45, which will eliminate all 3s on r1345789c45... And the puzzle will be solved easily...

All these thanks to your earlier suggestion that leads to this step...

PS: It seems Pyrrhon has deleted some of the puzzles from his website... I couldn't access te 123 and 234 puzzles anymore...
udosuk

Posts: 2698
Joined: 17 July 2005

General observation:

If you take a valid, completed, regular Sudoku grid, and change all the 4's and 7's to 1's, and all the 5's and 8's to 2's, and all the 6's and 9's to 3's, you have a valid, completed, 123 Sudoku grid.

But the original clue set, converted as above, will probably no longer be sufficient to establish a unique solution.

As I recall, the maximum number of clues in an independent clue set is known to be somewhere in the 30's, and the thought-to-be-minimum is 17. Has anybody given any thought (shudder) to what the maximum and minimum might be in the 123 case? I assume both would be higher than for regular Sudoku.

Bill Smythe
Last edited by Smythe Dakota on Wed Jul 19, 2006 7:11 am, edited 1 time in total.
Smythe Dakota

Posts: 564
Joined: 11 February 2006

There is a tacit agreement that there is a difference between 1-2-3 sudoku, 2-3-4 sudoku, 1-2-3-4 sudoku, 1-2-3-4-5 sudoku in one hand and 123 sudoku, 1234 sudoku in the other . The first group is where we have one 1, two 2's, three 3's or four 4's and the other group has the same number of 1's, 2's, 3's or 4's.

Pyrrhon
Pyrrhon

Posts: 240
Joined: 26 April 2006

I was not aware of that convention, but it seems as reasonable as any. I have edited my earlier post accordingly.

Bill Smythe
Smythe Dakota

Posts: 564
Joined: 11 February 2006

For proper closure of this thread I'll show all the possible solutions for this (now deleted) 123c puzzle... Turns out you could work out 58 cells and then there are altogether 5 different solutions coming out from the remaining 23 cells...

Original puzzle:

All the 58 cells you could work out (and candidates for the remaining 23):

Solution 1:

Solution 2:

Solution 3:

Solution 4:

Solution 5:
udosuk

Posts: 2698
Joined: 17 July 2005

I see I must make new ones of this variant. But it is really hard to make interesting sudoku of this kind. This is easier with the 1-2-3-4 variety.

Pyrrhon
Pyrrhon

Posts: 240
Joined: 26 April 2006

I have changed the opening sudoku of this thread with a valid one. It is called by udosuk 123a. And now two new ones:

Puzzle 123d:

Puzzle 123e:

Pyrrhon

Posts: 240
Joined: 26 April 2006

Spoiler warning:
If you haven't solved the puzzles and intend to solve them yourself, don't click on these links...

Puzzle 123d:

An x-wing followed by a turbot fish will solve it...

Solution

Puzzle 123e:

You could find an x-wing, but it's not really necessary... "Double locked candidates" in nonet 2 will do...

Solution
udosuk

Posts: 2698
Joined: 17 July 2005