1Definition: More of a procedure than a technique, Generating All Candidates involves filling in all of the possible candidates in each empty cell of the board. It is a prerequsite for all of the techniques which follow (i.e. all techniques beyond the Easy level.)
2Look For: Empty cells (i.e. cells which have no Big Number in them, but that may have candidate numbers already present.)
3Consequence: When all candidates are filled in for all empty cells, patterns can be discerned which will lead to erasing candidates until only one possible candidate remains in a cell -- and that number will then become a Big Number: the solution to the cell.
4Why it Works: Once you see all the possibilities you can use pattern-recognition to solve the puzzle.
A medium-level puzzle with all candidates filled in.
6Here is an example from a medium-level puzzle, after all the easy techniques have been applied. Hard candidates have been entered during crosshatching, but none of the easy techniques will yield any more Big Numbers at this point. So, it is time to generate all candidates.
7We have simulated turning on the Highlight House on Hover tool, and then hovering over cell A1. This highlights A1's house, making it easier to see all the numbers that can't be candidates for this cell.
Can be a 3 (as no 3 appears in A1's house, and the hard-candidate 3 on H1 is vertical only.)
Cannot be a 4 (due to C1.)
Cannot be a 5 (due to C3, as well as I1. [The hard-candidate 5's on A6 and A8 have no effect since they are horizontal only.])
Cannot be a 6 (due to B3, as well as the hard-candidate 6's on G1 and H1.)
Can be a 7 (as no 7 appears in A1's house.)
Cannot be an 8 (due to B1, as well as A7.)
Cannot be a 9 (due to the hard-candidate 9's in block 1 on B2 and C2, as well as the 9 on D1.)
9So we enter little numbers 3 and 7 in cell A1. These are regular (or "soft") candidates: unlike hard-candidates, by themselves they do not restrict any other cells from being 3's or 7's. They just relate to A1, and say that this cell will contain one of these numbers when solved.
10Normally, you would proceed methodically through each empty cell in order. But we're going to just pick a few to do here, to illustrate a point, and then let you try one.
11Let's take a look at B2. Highlighting it's house, we quickly see that numbers 1-6 are in its house, and so are unavailable to this cell. But 7 and 9 are available. Since 9 is already there, as a hard-candidate, we just enter a 7.
13Now let's see what happens when we generate all candidates for G2. Highlighting its house, we see that every number is accounted for except for number 7 [Don't forget that the horizontal hard-candidate 9's in B2 and C2 have claimed 9 for Block 1 in row 2; so the 9 cannot be a candidate here in Block 3.] So, we enter a little 7 in the G2. However, since it is the only possible candidate for the cell, we can go ahead and treat it right now as a Single Possibility (or as a Naked Single: a technique we'll cover in a later tutorial), and enter a Big Number 7.
14This causes one of those nice little chain-reactions that make Sudoku so much fun, as all of the 7's in this cell's house can now be erased. This leaves a lone hard-candidate 9 in B2, so we enter a Big Number 9 there. This, in turn, eliminates the 9 from C2, leaving a lone 3 in that cell. So, we enter a Big Number 3 in C2. This eliminates all 3's from C2's house -- including the horizontal hard-candidate 3 in C4, which, in turn, forces A4 to be a Big Number 3. Then, we come full circle, as the 3 in A1 is eliminated, and A1 becomes a 7!
15Your Turn! Now it's your turn to try one. We have highlighted D9's house for you. The hard-candidate 2 has already been done for you, so leave that alone. You will be entering 3 other candidates in cell D9.
17Great job! Here is a tip for entering all candidates. Instead of row by row, do a Block at a time. First see what Big Numbers and hard-candidates already exist in the Block. Then mentally list the remaining numbers. Now, for each empty cell in the Block, mentally go through this list of remaining numbers, and only scan along the cell's Row and Column to see if the number exists. This gives you only two things to check ( the Row and the Column) instead of three (the Row, Column, and Block.)
18For instance, look at Block 5. The remaining numbers there are 4, 6, and 8 (the rest being accounted for as Big Numbers or hard-candidates.) In the first empty cell of the Block: D4 we don't find a 4, 6, or 8 in row 4 or column D, so we enter all three of these numbers in the cell as candidates. In the next empty cell (E4) we find a 6 in the column, so we enter just the 4 and 8 in this cell. In F4 we find both a 4 and an 8 in the column, so we only enter a 6 in the cell. In the last empty cell of the Block (D6) we enter all three candidates.
19Sometimes while Generating All Candidates we solve the cell! For instance, in Block 2 we see that 7 is the only remaining number (the rest are already accounted for as Big Numbers or hard-candidates.) Looking at empty cell E1 we see a 7 at A1, so we know the 7 cannot go in E1, and therefore we can enter a Big Number 1 in E1 right now! Looking at the next empty cell in Block 2 we don't see a 7 in row 3 or column D, so we enter a candidate 7 in D3, and another 7 in E3. Since D3 is the only 3 in Block 2 we can convert it to a Big Number 3, leaving E3 to become a Big Number 7.
20Generating All Candidates is a skill you need to have for all but the simplest of puzzles. You will need it, of course, for any hard-copy puzzles you do with paper and pencil. However, most online implementations (including SueDoku) offer to Generate All Candidates for you! (In SueDoku there is the Fill in All Candidates button on the Tools tab [not available in the tutorials.]) This gives you the option of skipping a step which some perceive as tedious, and get to the more exciting pattern-matching part of the game.
21While we recommend using the techniques of Crosshatching, Full-House, Single-Possibility, and Hard-Candidates until they yield no more results before Generating All Candidates (especially with pencil and paper, as these techniques will cut down on the number of cells needing full candidate generation), some will prefer to start out immediately with Generating All Candidates when playing online. This is perfectly okay, as there is nothing these easy techniques can do that techniques following Candidate Generation would miss.
22Whatever you decide to do, just keep in mind the best thing about Generating All Candidates is that, unlike the other techniques, you only have to do it once per puzzle! Once you do it you won't be entering any more candidates; only erasing them to get down to single candidates per cell!
This is the end of the Generate All Candidates tutorial.
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