- Code: Select all
.---------------------.-----------------.-----------------------.
| 45789 34789 36789 | 789 2689 d267 | 56789 36789 1 |
| 5789 789 2 | 1789 e1689 3 |f56789 4 789 |
| 789 1 36789 | 789 4 5 | 6789 236789 23789 |
:---------------------+-----------------+-----------------------:
| 14789 24789 1789 | 34 2389 247 | 789 5 6 |
| 3 789 5 | 1789 1689 c167 | 2 789 4 |
| 6 24789 789 | 45 2589 247 | 3 1 789 |
:---------------------+-----------------+-----------------------:
| 1789 3789 13789 | 2 13 b14 |a146789 6789 5 |
| 129 5 4 | 6 7 8 | 19 239 239 |
| 1278 6 1378 | 345 135 9 | 1478 278 278 |
'---------------------'-----------------'-----------------------'
4r7c7 = (4–1)r7c6 = (1–6)r5c6 = r1c6 – r2c5 = 6r2c7 => –6r7c7
Suppose -13r7c23.
- Code: Select all
.---------------------.-----------------.---------------------.
| 4–5789 3–4789#6789–3| 789 2689 267 | 5789–6#789–3 1 |
| 5–789 #789 2 | 1789 1689 3 | 56789 4 #789 |
|#789 1 3789–6| 789 4 5 |#6789 23789 23789 |
:---------------------+-----------------+---------------------:
|#789–14 24789 1–789 | 34 2389 247 |#789 5 6 |
| 3 #789 5 | 1789 1689 167 | 2 #789 4 |
| 6 24789 #789 | 45 2589 247 | 3 1 #789 |
:---------------------+-----------------+---------------------:
| 1789 789 789 | 2 13 14 | 14789 6 5 |
| 129 5 4 | 6 7 8 | 19 239 239 |
| 1278 6 3–178 | 345 135 9 | 1478 278 278 |
'---------------------'-----------------'---------------------'
HS 3b7, 1c3, 3b1, 4b1, 5b1
TH 789b1346 internals 6r1c3, 6r3c7 => –6r3c3, –6r1c7
- Code: Select all
.-------------------.-----------------.---------------------.
| 4 3 6–789| 789 2689 267 | 56789 a789 1 |
| 5 c789 2 | 1–789 6–189 3 | 56789 4 789 |
| 789 1 789 |b789 4 5 | 6789 23789 23789 |
:-------------------+-----------------+---------------------:
| 789 24789 1 | 34 2389 247 | 789 5 6 |
| 3 d789 5 |d789–1 1689 167 | 2 d789 4 |
| 6 24789 789 | 45 2589 247 | 3 1 789 |
:-------------------+-----------------+---------------------:
| 1789 789 789 | 2 13 14 | 14789 6 5 |
| 129 5 4 | 6 7 8 | 19 239 239 |
| 1278 6 3 | 45 15 9 | 1478 278 278 |
'-------------------'-----------------'---------------------'
HS 6b1, 6b2, 1b2
the digit in r1c8 is forced into r3c4 in b2, r2c2 in b1 and eliminated out of the 789 triple in r5c248, ie. contra.
Therefore (1|3)r7c23, virtual pair 13r7c235 => -13r7c167.
- Code: Select all
.---------------------.--------------.---------------.
| 4789 34789 3789 | 789 2 6 | 5 x–yz 1 |
| 5 yz789 2 | 1 x89 3 | 6 4 yz789 |
|x789 1 6 | 789 4 5 | 789 23 23 |
:---------------------+--------------+---------------:
| 14789 24789 1789 | 34 389 27 | 789 5 6 |
| 3 yz789 5 |x89 6 1 | 2 yz789 4 |
| 6 24789 789 | 45 589 27 | 3 1 x–yz|
:---------------------+--------------+---------------:
| 789 3789 13789 | 2 13 4 |x789 6 5 |
| 29 5 4 | 6 7 8 | 1 239 239 |
| 1278 6 x1378 | 35 135 9 | 4 278 278 |
'---------------------'--------------'---------------'
Let x be the digit in r2c5 and yz be the remaining digit among 789.
HS xc4; remote pair yzr25 => –yzr1c8, -yzr6c9 => NS xr1c8, xr6c9; HS xb1, xb9, xb7
x appears both in r2c5 and r9c3 => x=8, stte
ghfick wrote:I am curious if one or more of these 12 cells could contain fewer than the three digits.
The pattern doesn't rely on uniqueness. It simply doesn't have a solution.
When you remove some of the candidates (whether during the solve or in the initial state), the number of solutions obviously cannot increase, so it still won't have a solution.
That means that any missing candidates have no effect on its eliminations.
Marek