## Pseudoku

For fans of Killer Sudoku, Samurai Sudoku and other variants

### Pseudoku

We had a discussion about pseudoku here. I will give a new example:

Fill in the grid so that every row/column contains all the numbers from 1 to the length of that particular row/column.

Have fun.

Pyrrhon
Pyrrhon

Posts: 240
Joined: 26 April 2006

Interesting

It can also be viewed as a Latin square where the missing triangle is filled with 9s,8s... like this

Jean-Christophe

Posts: 149
Joined: 22 January 2006

Nice observation, it seems to be a consequence of the diagonal symmetry of the grid.

Pyrrhon
Pyrrhon

Posts: 240
Joined: 26 April 2006

So, a Latin square is nothing more than a sudoku without the boxes?

Bill Smythe
Smythe Dakota

Posts: 564
Joined: 11 February 2006

Smythe Dakota wrote:So, a Latin square is nothing more than a sudoku without the boxes?

yes, but the timeline is the other way: a sudoku is a latin square with box constraints
also, references to QWH (quasigroup with holes) in older forum threads mean "latin square" solving
gsf
2014 Supporter

Posts: 7306
Joined: 21 September 2005
Location: NJ USA

Pyrrhon, I wanted to play with your puzzle using my soft, so I turned it into a Latin square.

Hint : a swordfish will unlock it

Bill, yes a Latin square is like a sudoku without boxes. See also Wikipedia : http://en.wikipedia.org/wiki/Latin_square
Jean-Christophe

Posts: 149
Joined: 22 January 2006

gsf wrote:.... yes, but the timeline is the other way: a sudoku is a latin square with box constraints ....

I figured it would be.

Also, for a short time I was confusing latin squares with magic squares. Is it true that, if you have a 9x9 latin square, you can convert it to a magic square by adding 9*(r-1)+9*(c-1) to each cell? For example, you'd add 0 to r1c1, 9 to r1c2 and r2c1, 18 to r1c3 and r2c2 and r3c1, etc?

(I haven't really given this a whole lot of thought, so maybe I'm just being incredibly stupid.)

Bill Smythe
Smythe Dakota

Posts: 564
Joined: 11 February 2006

I wrote:.... Is it true that, if you have a 9x9 latin square, you can convert it to a magic square by adding 9*(r-1)+9*(c-1) to each cell? For example, you'd add 0 to r1c1, 9 to r1c2 and r2c1, 18 to r1c3 and r2c2 and r3c1, etc? ....

Oops, that's dumb. If, for example, r1c4 and r4c1 have the same digit to begin with, they'd still be the same in the resulting not-so-magic square.

But there must be SOME formula along those lines. Since a Sudoku has an average value of 5, whereas a 9x9 magic square has an average value of 41, you'd have to add an average of 36 to each cell. Can anybody come up with a formula?

By the way, do I have the right idea of a magic square? I'm thinking that each value, 1 through N-squared, must appear exactly once, and that the sum of each row and column must be the same (369 in the 9x9 case). I hope the main diagonals aren't also supposed to be the same, that would be a major monkey wrench.

Bill Smythe
Smythe Dakota

Posts: 564
Joined: 11 February 2006

Jean-Christophe wrote:Hint : a swordfish will unlock it

An extra hint:

A swordfish of 5 followed by a naked quad/hidden pair on column 3 will completely solve it...

Here is the solution:

539872614
796283451
968517342
187946523
87265413
6547312
421365
34512
2134

udosuk

Posts: 2698
Joined: 17 July 2005

Here a little addition. This give-away is called Pseudo Fun. It requires no given digits and is a valid Pseudoku. Empty diagrams can't be copyrighted. So this one is freeware.

Pyrrhon

Fill in the grid so that every row/column contains all the numbers from 1 to the length of that particular row/column.

Pyrrhon

Posts: 240
Joined: 26 April 2006

This one is terribly hard to solve
Required ... 5 miliseconds
Jean-Christophe

Posts: 149
Joined: 22 January 2006

The need for symmetry and a single solution makes it obvious.
HATMAN

Posts: 275
Joined: 25 February 2006
Location: Nigeria

Pyrrhon wrote:Here a little addition. This give-away is called Pseudo Fun. It requires no given digits and is a valid Pseudoku. Empty diagrams can't be copyrighted. So this one is freeware

Is this a joke ??? It lives up to its name alright

tarek

tarek

Posts: 3759
Joined: 05 January 2006

It was planed that jcbonsai can solve it in 5 ms. Only binary sudoku is easier. Isn't it?

Pyrrhon
Pyrrhon

Posts: 240
Joined: 26 April 2006

Pyrrhon wrote:It was planed that jcbonsai can solve it in 5 ms. Only binary sudoku is easier. Isn't it?

Not true. The following puzzle should be the undisputed world champion :

How many milliseconds do you need, JC?
udosuk

Posts: 2698
Joined: 17 July 2005

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