## algebraic sudoku

For fans of Killer Sudoku, Samurai Sudoku and other variants

### algebraic sudoku

while I'm here, I might as well re-promote my 'algebraic sudoku' - which gives clues as algebraic relationships between the numbers in different squares:
http://sudokuguyblog.blogspot.com/search/label/algebraic%20sudoku

..just 'coz I think it's dorky-cool
sudokuguy

Posts: 8
Joined: 02 January 2007

This could be a variant I could sink my teeth into. Gonna try one out.

Hmm...after printing out your 6x6, I noticed a couple of AB's, which by your coordinate system are impossible.

Editing further, I've noticed that trying to combine equations is just about futile. I've figured out more just by putting in pencil marks. However, that's not yielding much info very quickly either.
JL

Posts: 36
Joined: 19 December 2006

eek! you are right ... thanks for catching that!

those AB's should have been BG's in both cases. I think you'll find the puzzle makes sense now:
http://sudokuguyblog.blogspot.com/2007/05/mini-algebraic.html

by the by ... I doubt you can solve the puzzle by doing parallel equations! use pencil marks to eliminate the candidates in each cell.
sudokuguy

Posts: 8
Joined: 02 January 2007

Sudokuguy

Very enjoyable - I'm working my way through them.

I know you're not keen on killers but for anyone else who enjoys these puzzles ZD has come up with a killer variant (on DJApe's forum) where you are told the cage totals (not sums) and have to work out the operators as well as the numbers. Following your lead we call them Algebraic Killers - see http://www.djape.net/sudoku/forum/viewtopic.php?t=1008

HATMAN
HATMAN

Posts: 207
Joined: 25 February 2006

sudokuguy wrote:by the by ... I doubt you can solve the puzzle by doing parallel equations! use pencil marks to eliminate the candidates in each cell.

Yeah, I just found myself going in circles. I'm gonna try that 6x6 later. I was working on one of the larger ones earlier and found myself eliminating possibilities from the wrong cell. Whoops.
JL

Posts: 36
Joined: 19 December 2006

I love the idea, and they're great puzzles (including the 9x9 ones)!

However, I find it a bit uncomfortable to use the "all-letters" indices. It'd be much easier for me to spot the cells quickly if the column indices are in digits instead. So I've redrew your 6x6 one:

(Note I've also shaded all cells involved in equations in yellow.)

Here is a brief walkthrough plus the solution:

b4=c5-e2 => c5>1
c2=c5xd5 & c2<>c5 => d5>1
=> {c5,d5}={2,3}, c2=2x3=6
d5=a1-b1=2|3 => a1>2 & a1>b1+1
e3=a1xb1>(b1+1)xb1 & e3=1..6
=> b1<2 => b1=1 => a1=d5+1=3|4
b4=c5-e2>1 => c5=3, e2=1, b4=2
=> d5=2 => a1=d5+1=3 => e3=a1xb1=3
c3=c4-a3 => c4>1 => c4=4|5
=> a3<5 => a3=2|4
=> c3=c4-a3<4 => c3=1|2
a3<>c3 => [c3,c4,a3] can't be [2,4,2]
=> c3=1, c4=5, a3=4
d4=a5/e1 & e1>1 => d4<4 => d4=1
=> a4=6 => a5=e1=5

The rest is trivial.

324651
156243
261534
435126
513462
642315

udosuk

Posts: 2698
Joined: 17 July 2005

udosuk said:
However, I find it a bit uncomfortable to use the "all-letters" indices. It'd be much easier for me to spot the cells quickly if the column indices are in digits instead.

..I hear ya - but I decided using numbers as indices would be too confusing since there are actually numerical operations in the puzzle. by using only letters as indices, you know that whenever you see a number it actually functions as *that number* not a reference to something else.
sudokuguy

Posts: 8
Joined: 02 January 2007

I've no problem with numbers as indices. Maybe it's the many math classes with variables like x1, x2, ..., xn where the numbers are subscripted. My mind just automatically subscripts the numbers, and the confusion is eliminated.
JL

Posts: 36
Joined: 19 December 2006

I tend to agree with JL here. I think anybody who studied maths in highschool should be okay with something like "c5-e2" and wouldn't confuse it as "5-2". However if sudokuguy wants to cater for everybody including the mathematical challenged (why they want to attempt an "algebraic sudoku" puzzle in the first place I have no idea) then I guess you can stick with your current system. I guess it takes some time for us to get used to your "all-letters" system while the "letter-number" system are already familiarised by many of us (e.g. maths classes, chess notation, spreadsheet). Many sudoku players do use the "letter-number" system to denote the cells instead of the more conventional "r#c#" system.
udosuk

Posts: 2698
Joined: 17 July 2005

hey I don't want to start a big 'numbers vs letters' controvosy here! whatever nomination you prefer, floats my boat.

the fact is that when I started making these puzzles, the formulas in the cells would also include actual numbers, and not just references elsewhere. eg - a formula could be AGx5, or 3-BL. I thought in that case, it was best to keep the numbers (as numbers) and the letters (as identifiers) separate. sinc then, I've eliminated the bare numbers and moved on to an all-reference puzzle.

so, we could call them dogs and elephants for all I care. but I agree that numbers for columns and letters for rows is a more 'conventional' notation, so OK. let's use that.
sudokuguy

Posts: 8
Joined: 02 January 2007

I like to add an exemple for Algebraic Sudoku X here:

Fill in the grid so that every row, every column, every 3x3 box and both diagonals contains the digits 1 through 9. The algraic operations in the cells must be fullfilled.

Pyrrhon

Posts: 240
Joined: 26 April 2006

*laugh* Of course, where there's a new variant, there's an X-new variant.

I've been having a bit of trouble with these puzzles. More than likely it's my bad bookkeeping skills, but I keep running into invalid puzzles. Tried to get through sudokuguy's 4th puzzle a couple times to no avail.

Anyone else that can relate, or do I just suck that bad?
JL

Posts: 36
Joined: 19 December 2006

Nobody had said that Algebraic X is a new variant. But the X allows a greater variety of techniques and so it is frequently interesting to have a x puzzle.

Sudokuguys algebraic sudoku 4 has a unique solution. This is:

437582619
812936754
659471328
126798435
574623891
983154267
265849173
741365982
398217546
Pyrrhon

Posts: 240
Joined: 26 April 2006

Argh...I meant puzzle 3, but at least people are coming up with solutions.

Sorry for the confusion, Pyrrhon. What I meant is that almost invariably someone puts X constraints on a variant, ie

'Vanilla' Sudoku -> Sudoku X
Killer Sudoku -> Killer X
Algebraic Sudoku -> Algebraic Sudoku X

And so on. And it's cool. I've almost given up on these puzzles, though. Don't know what I'm missing that I keep screwing up.
JL

Posts: 36
Joined: 19 December 2006