forum.enjoysudoku.com/help-almost-locked-candidates-move-t37339.html
A while back, yzfwsf added these techniques to his software, YZF_Sudoku. YZF_Sudoku is an excellent learning tool for human solvers and it has the largest number of techniques to date. It turns out that these two techniques pop up quite often in YZF_Sudoku's solution paths.
Here is an example of an Almost Locked Pair [ALP]:
6....7..4..45..7...9..4..8..8.2....3..3...2..5....3.1...1.9..6.4....51...6.3....2
- Code: Select all
.------------------.----------------------.-------------------.
| 6 1235 258 | 189 1238 7 | 359 2359 4 |
| 1238 123 4 | 5 12368 12689 | 7 239 169 |
| 1237 9 257 | 16 4 126 | 356 8 156 |
:------------------+----------------------+-------------------:
| 179 8 679 | 2 1567 1469 | 4569 4579 3 |
| 179 147 3 | 146789 15678 14689 | 2 4579 56789 |
| 5 247 2679 | 46789 678 3 | 4689 1 6789 |
:------------------+----------------------+-------------------:
| 2378 2357 1 | 478 9 248 | 3458 6 578 |
| 4 237 2789 | 678 2678 5 | 1 379 789 |
| 789 6 5789 | 3 178 148 | 4589 4579 2 |
'------------------'----------------------'-------------------'
Consider the line r3 and the block b3. Since r3c4 is a bi-value cell [16], the mini-line r3b3 can contain at most one of {1, 6}. But now notice in the first two rows of b3, {1,6} appears only once [in r2c9] and so the mini-line r3b3 must contain at least one of {1,6}. The "at most" and the "at least" mean the the mini-line r3b3 must contain exactly one of {1,6}. We then see that r3c4 and r3b3 form what is often called a virtual locked pair. So, in the line r3, we can exclude {1} from r3c1 and r3c6 and we can exclude {6} from r3c6. In addition, since r2c9 must contain one of {1,6}, we can exclude {9} from r2c9.
It is true that these same exclusions can be seen from a Sue de Coq or and ALS-XZ but the ALP argument seems far easier to me. YZF_Sudoku rates ALP as 'Hard' [yellow] and I agree with this rating.
Now, let's consider an example of an Almost Locked Triple [ALT] :
5..9..3...3......4....6..8.1..4.2.....2.3.......5.67..6....98....8.....1.4.....3.
- Code: Select all
.--------------------.---------------------.----------------------.
| 5 12678 1467 | 9 12478 1478 | 3 1267 267 |
| 2789 3 1679 | 1278 12578 1578 | 12569 125679 4 |
| 2479 1279 1479 | 1237 6 13457 | 1259 8 2579 |
:--------------------+---------------------+----------------------:
| 1 56789 35679 | 4 789 2 | 569 569 35689 |
| 4789 56789 2 | 178 3 178 | 14569 14569 5689 |
| 3489 89 349 | 5 189 6 | 7 1249 2389 |
:--------------------+---------------------+----------------------:
| 6 1257 1357 | 1237 12457 9 | 8 2457 257 |
| 2379 2579 8 | 2367 2457 3457 | 24569 245679 1 |
| 279 4 1579 | 12678 12578 1578 | 2569 3 25679 |
'--------------------'---------------------'----------------------'
Consider the line r5 and the block b6. In b6, the cells r4c7 and r4c8 contain only {5,6,9}, so r5b6 can contain at most one of {5,6,9}. But now notice that, in r5, {5,6,9} appear in only r5c1 and r5c2. So r5b6 must contain at least one of {5,6,9}. Again, the "at most" and the "at least" mean that the mini-line r5b6 must contain exactly one of {5,6,9}. This observation gives 10! exclusions. Again, these same exclusions can be seen from [the much harder to see] Sue de Coq or the ALS-XZ.
The ALT argument is the same as the ALP argument. ALT is certainly tougher to see than an ALP. Human solvers search for exclusions using the bi-value cells early in solving. The search for exclusions using ALS is certainly harder but the ALT seem among the easiest of ALS exclusions.
Notice, that with ALP, the bi-value cell can be in the line or the block. With ALT, the ALS can be in the line or the block. This is detailed in the forum post noted above.
