## A pleasing deduction

Advanced methods and approaches for solving Sudoku puzzles

### A pleasing deduction

Hmm, I played one of the 2x4 Su Dokus from rubylips' site...

Code: Select all
` 5 . | . . | 1 . | 8 . . . | . . | . . | . . 6 . | 7 . | . . | . 2 . . | 3 . | . 4 | . .----------------------- . . | 8 . | . 5 | . . 7 . | . . | . 6 | . 4 . . | . . | . . | . . . 2 | . 1 | . . | . 3`

... and was very pleased with the stage that immediately follows at this point:

Code: Select all
` 5 . | . . | 1 . | 8 . . . | 1 . | . . | . . 6 . | 7 . | . . | . 2 . . | 3 . | . 4 | . .----------------------- . . | 8 . | . 5 | . . 7 . | . . | . 6 | . 4 . . | . . | . 1 | . 8 . 2 | . 1 | . . | . 3`

Here I relabel four of the blank cells A, B, C and D:

Code: Select all
` 5 . | . . | 1 . | 8 . . . | 1 . | . . | A . 6 . | 7 . | . . | B 2 . . | 3 . | . 4 | C D----------------------- . . | 8 . | . 5 | . . 7 . | . . | . 6 | . 4 . . | . . | . 1 | . 8 . 2 | . 1 | . . | . 3`

Now clearly either B, C or D is the position for 1 in the top-right box. But observe that A and B are 3 and 4 in some order. So either C or D is 1. Suppose C is one; one can see almost immediately that this would prevent a 1 being entered in the bottom-left box. It follows that D must be 1. The puzzle progresses from there to a unique solution.

What is the name of the technique I used? I was very pleased to find it.
Hammerite

Posts: 44
Joined: 20 June 2005

### Re: A pleasing deduction

Hammerite wrote:What is the name of the technique I used? I was very pleased to find it.

I'd call it a hidden pair in cells A & B.
Then it'd be eliminating candidates (in this case 1s) in row 4.
Then it'd be hidden singles (in this case 1) in column 1.
Then it'd be hidden singles (1 again) in cell D.

angusj

Posts: 306
Joined: 12 June 2005

Oh, ok. So not very advanced, then! Still... it pleased me *shrug*

(I'm not very good with the terminology, but your site helped me to see what you meant. Thanks!)

Oh, technically the fourth sentence in the second-to-last paragraph of my original post was not really what I meant to say. A correct thing to say, given the way I was looking at the problem, was "Suppose C is 1; one can see almost immediately that this allows the placement of only two other 1s in the other three corner boxes, though three are required".
Hammerite

Posts: 44
Joined: 20 June 2005

Hammerite wrote:Still... it pleased me *shrug*

Don't you hate it when some smartypants comes along and suggests you've just reinvented the wheel - especially when you've spend a long time waiting for that 'ah ha' moment.

Hammerite wrote:I'm not very good with the terminology

I don't think there is an agreed terminology - just use what make sense to you (and hopefully to others).
angusj

Posts: 306
Joined: 12 June 2005