This is how i do hard and worse sudokus

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Basically there are 2 main stages in my solving teqnique:

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1) Solve as much as possible of the sudoku, without writing down all candidates. Write down multiple candidates selectively during this process...

The main Idea is to find a process where you scan the most promising information first. And scan the same information as few times as possible, writing down the information at the right time, without cluttering the board unnecessarilly.

2) Sudoku partially solved, non-fixed squares have all candidates written in the square. Squares with only 2 candidates have a pencilled square around the pair. (Simplifies spotting forcing chains).

Terminology:

HOUSE: box or row or column

1)

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Go by numbers.

Start with a number that intuitevly seems most promising.

When finished with that number, write it down on the side. Take

the next number that has not been written down that seems most promising.

For each number, check for givens, apply as advanced logic as you want, given the information on the board. When done, make a judgement if you want to write down all remaining candidates for this number (the whole board). If they are few, write them down in the squares. Check for nishio, x-wing, etc. If the candidates are many, don't write them down yet.

Note your progress:

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* Was the number too hard? then do NOT write it down on the side.

Return to it later.

* Did you make progress, but did not write down the remaining candidates? Write down the number on the side, WITHOUT circling it.

* Did you write down all remaining candidates? (For the whole board)

Then write down the number on the side WITH a circle around it.

Take a new number, that has not been written down on the side.

Repeat until all numbers have been written down on the side.

During your progress, if you can prove that a cell only has 2 candidates,

draw a square around those candidates.

*BREATHER*

You will now have a list to on the side with numbers 1-9, some circeled, some not. The numbers with circles have all their possible candidates written in the cells of the board.

If you have more than 3 uncircelled numbers, reduce that number to 3.

All numbers, except these 3 should now have their candidates written on the board. These 3 numbers will be called a,b & c

Check for empty squares.

If yo have done things right up to now, empty squares can only hold (a,b, or c)

For each empty square, test for a,b&c. Chances are good that you quickly will find a few doubles. (ab, ac, or bc) Square these.

Complete each box.

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For each box, fill in candidates for a,b & c. (Don't check your squared doubles. You have already proven that they are complete. That's why you squared them) When a box is done, mark it

by pencilling the upper left edge.

You can also complete the box earlier if feasible. Remember to

pencil-mark the box only if all caldidates for all numbers have been checked in that box.

Remember to only circle a number on the side if candidates for that number have been written down for ALL boxes.

Step 1 DONE.

All candidates have now been filled in. During the whole process. Focus on recognizing nishio's and forcing chains. The fact that the bulk of the work is done number by number, makes it easier to recognise nisho and other number-specific patterns at an early stage.

2) Here you're on your own

Hopefully you have already cracked a nishio, forcing chain, or fishy cycle before you get here.

ADVANTAGES:

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Spotting hidden pairs: If number x and y populate the same 2 squares, and no other squares in a house, then these are a pair. You may happen spot this early before other candidates have been written down in the house.

Spotting x-wings and other number-specific patterns.

Since the bulk of the candidate entry is done per number not per house, the mind easier recognizes these patterns.

Variations:

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Write down candidates in only a few boxes. Good if you spot a box-row intersection that leads to reductions in a certain box, and you want to remember that, but the candidates for that number are too many in the other boxes. Remember to NOT circle the number on the side.

Disadvantages.

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Squaring double candidates sometimes causes me to miss them when

I am scanning rows and columns. This is because I initially wirte the candidates small in their respective position within the cell (divide the cell in a 3x3 grid), but if find a pair, I erase the small numbers and write the pair larger in the middle of the cell (with a square around)

That's my technique.

EDIT:

I can add that I break this process anytime when I find something useful that is wirth pursuing right away. This is no problem. My pencil-marked-boxes and numbers-on-the-side still apply and tells me where to continue when I get stuck again...