Consider the following grid:
- Code: Select all
*-------.--------------.-------*
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | 1234 14 1234 | . . . |
.-------.--------------.-------.
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
.-------.--------------.-------.
| . . . | 23 . 234 | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
*-------.--------------.-------*
From my analysis, I've discovered that if r7c6 is 4, then r12c6 cannot be 4. Conversely, if r7c6 is not 4, it creates a UR type 3, leading to the conclusion that r12c6 must not be 4. Similarly, if r7c6 contains 1, 2, or 3 only, then r12c6 must not be 1.
Now, let's examine another grid:
- Code: Select all
*-------.--------------.-------*
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | 1234 14 1234 | . . . |
.-------.--------------.-------.
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
.-------.--------------.-------.
| . . . | 123 . 234 | . . . |
| . . . | 234 . 123 | . . . |
| . . . | . . . | . . . |
*-------.--------------.-------*
In this case, we can observe that we can split the 8th box into 4 cases:
Case 1:
r7c4=1, r8c4=4, [2, 3] pair on r78c6
=>> [1, 4] pair on r3c56
=>> Remove 1/4 at r12c456 and r3c123789
Case 2:
r7c6=4, r8c6=1, [2, 3] pair on r78c4
=>> [1, 4] pair on r3c45
=>> Remove 1/4 at r12c456 and r3c123789
Case 3:
r7c4=1, r7c6=4, [2, 3] pair on r8c46
=>> UR type 3 at r38c46
=>> Remove 1/4 at r12c456 and r3c123789
Case 4:
r8c4=4, r8c6=1, [2, 3] pair on r7c46
=>> UR type 3 at r37c46
=>> Remove 1/4 at r12c456 and r3c123789
In each of these cases, the same result can be achieved, indicating that r12c456 and r3c123789 must not contain 1 or 4.
Similarly, we can apply this strategy to remove 1/4 from cells r1c4, r1c5, r1c6, r2c4, r2c6, and r3c5 in the following grid:
- Code: Select all
*-------.--------------.-------*
| . . . | . . . | . . . |
| . . . | . 14 . | . . . |
| . . . | 1234 . 1234 | . . . |
.-------.--------------.-------.
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
.-------.--------------.-------.
| . . . | 123 . 234 | . . . |
| . . . | 234 . 123 | . . . |
| . . . | . . . | . . . |
*-------.--------------.-------*
Of course, the 2nd box can change to the following forms, these 2 types of UR still work while a and b are different numbers:
- Code: Select all
*---------------*
| . . . |
| . 14a . |
| 1234 14a 1234 |
*---------------*
*----------------*
| . 14ab . |
| . 14ab . |
| 1234 14ab 1234 |
*----------------*
etc. They are still work while adding c, d, e with the same pattern.
That's it. I need more feedback, thank you.
