1Definition: Hard-candidates are candidates that must go in one of two cells in the same lane and block.* Most Hard-Candidates can be easily found early on, during the cross-hatching phase, prior to (or -- in the case of easy puzzles -- in lieu of) the sometimes tedious step of generating all candidates for all cells.
Vertical Hard-Candidate 5 at D1 and D2.
2Look For: A candidate number that is restricted to a pair of cells in a block along the same lane.
The hard-candidate pair of cells "claims" the candidate number for the lane: the candidate cannot appear in this lane outside of this block, and so can be eliminated as a candidate from the other two blocks along the lane.
The hard-candidate can act exactly as a Big Number when cross-hatching.
When one of the hard-candidates in the pair is eliminated, the other hard-candidate can be changed to a Big Number without a further thought!
In certain situations they can reveal matching pairs early on: effectively eliminating all other candidates from their cells.
4Why it Works: When a candidate is identified as belonging in one of the three blocks of a lane, it cannot possibly go in either of the other two blocks. So, in regards to the lane, the hard-candidate can act as if it were a Big Number in most situations.
Discovering hard-candidate 1 on B5/C5 via cross-hatching
6In the figure above, the hard-candidates 2, 4, 5, and 8 (in rows 1 and 2 of columns A, D, and G) have been previously entered during crosshatching. Crosshatching of these numbers did not yield a single cell, but rather two cells in the same lane (in these cases the same column.) In such situations a hard-candidate can be entered in bold, using the prime symbol (the apostrophe: ') next to the candidate to show that one of these cells owns the candidate along the column (i.e. vertical hard-candidates.)
7Now, we have just crosshatched horizontal band 2 for 1's. This has revealed two available cells in block 4 along the same row (row 5). So, we enter hard-candidate 1 in B5 and C5..This time we underline the hard-candidates, to show that they claim the candidate for this block along this row (i.e. horizontal hard-candidates.)
8What good does this do us? It does an immediate good turn for us: the hard-candidates we just entered act as Big Numbers when we crosshatch for 1's again in horizontal band 2. This gives us the Big Number 1 in D4.; something we would not have gotten at this point from simple crosshatching without using hard-candidates.
9The next crosshatching that yields results in horizontal band two is number 4. Crosshatching for 4's, we see two available cells in block 5 that are on the same row. So, we enter the horizontal hard-candidate 4's at E5 and F5.Crosshatching for 4s again, our new hard-candidates eliminate row 5 from consideration, leaving one open cell in block 6. So, we enter a 4 in G4. (Without the hard-candidates we wouldn't have known to do this.)
10Your Turn! Now it's your turn to try one! Crosshatch for 6's in horizontal band 2. Then enter the horizontal hard-candidates in block 5. (One way to do this is to hover over the 6 position in the cell and press the U key on your keyboard.)
11 Good job! Now, make use of the hard-candidates you just entered while crosshatching for 6's in horizontal band 2 again. You will discover that there is now only one place a 6 can go in block 6. hover over the cell in block 6 and enter the Big Number.
15The only thing left to point out is that cells A1 and A2 demonstrate matching pairs: a more advanced concept, covered in an upcoming tutorial. But, it would be useful to mention a few things briefly here.
16Because these are hard-candidates, we already know that the 4 and 8 are limited to these two cells for column A and for block 1. Therefore, we know that A1/A2 will either be 4/8 or 8/4. So:
No other candidates should be entered in A1 or A2.
No other 4 or 8 should be entered anywhere in column A.
No other 4 or 8 should be entered anywhere in block 1.
If any 4 or 8 was previously entered anywhere else in column A or block 1, they should be erased.
As soon as any candidate is erased from A1 or A2, the solution to both cells will be known.
17FAQS Do we enter hard-candidates when there are two candidates in the block but they are on different lanes? No. Only enter hard-candidates when there are two in the same lane of the block.*
18Do the cells of the hard-candidate have to be adjacent to one another? No. There may be a cell between them.
19What if there are three candidates in the same lane and block? Although these would share some of the same characteristics as hard-candidates, identifying them as such could lead to confusion (e.g. when eliminating one of them you couldn't automatically make one of the others a Big Number.) For this reason we do not recommend flagging three candidates in a row as hard-candidates. They will be considered under the Locked Candidates technique, described in a later tutorial.
20Do horizontal (underlined) hard-candidates have any effect on columns? No. Horizontal hard-candidates only affect the row and the block they are in. Likewise, Vertical (primed) hard-candidates only affect the column and block they are in (they don't have any effect on rows.)
21Can I have more than two horizontal hard-candidates in a single cell (or more than two vertical hard-candidates in a cell)? If you have more than two of a given type of hard-candidate in a single cell, one of the candidates can be erased. Two of the candidates will form a matching pair, and everything else in the cell can be removed. Here is an example where three vertical hard-candidates appear in A9, all of which seem reasonable results of cross-hatching. However, since the 8 and 9 form a matching pair with A8, the 6 can be erased from A9 (as well as the soft-candidate 2's in both A8 and A9 -- which makes A7 a Big Number 6, and C7 a 2.)
Erasing third hard-candidate
This is the end of the Hard-Candidates tutorial.
* Note: The latest version of Sue now recognizes hard-candidates that do not line up along a lane within a block. These are "block-only" candidates, and can be indicated by circling the candidate (via the C key on your keyboard). These candidates have no effect outside of the block, but serve to remind you that should you erase one of them, the other will be true.
Block-Only Hard-Candidates circled: 4's in blocks 4 and 8; 3's in block 9.
Set your preferences here.
Entering Numbers on the Board
Candidates ("Little Numbers")
Entry
Solutions ("Big Numbers")
Keyboard
Shift Keyboard
Num Keypad
Mouse
Note: Green buttons are "press-and-hold". Release to end, or slide-off to lock (then click to unlock.)
Show
For Numbers
Big #s
Small #s
Conj. Pairs
BVCs
Select Drawing Type
Line
Alt.
Can.
Alt.
Cell
Alt.
Locked
Click links, or press Tab to move to next parg/link, enter to highlight parg or activate link.
Prev: 
