The New Sudoku Players' Forum

[keith]

Here is a partially solved puzzle:

Code: Select all

+-------------+-------------+-------------+
| 2   5   1   | 7   4   8   | 9   6   3   |
| 3   9   4   | 6   5   2   | 7   18  18  |
| 6   7   8   | 1   3   9   | 4   5   2   |
+-------------+-------------+-------------+
| 5   26  267 | 9   8   3   | 12  4   17  |
| 1   8   3   | 4   2   7   | 5   9   6   |
| 9   4   27  | 5   1   6   | 28  3   78  |
+-------------+-------------+-------------+
| 8   3   69  | 2   679 4   | 16  17  5   |
| 4   26  5   | 8   67  1   | 3   27  9   |
| 7   1   269 | 3   69  5   | 68  28  4   |
+-------------+-------------+-------------+


So far as I can see, it is a BUG with three 3-candidate cells. Can someone please explain if there is a BUG reduction?

R4C3 is <2>, or R9C3 is <6>, or R7C5 is <6>. Then, what?

Thank you,

Keith

(I already have the Unique UR and the W-wing, thank you.)

[re'born]

Here is a partially solved puzzle:

Code: Select all

+-------------+-------------+-------------+
| 2   5   1   | 7   4   8   | 9   6   3   |
| 3   9   4   | 6   5   2   | 7   18  18  |
| 6   7   8   | 1   3   9   | 4   5   2   |
+-------------+-------------+-------------+
| 5   26  267 | 9   8   3   | 12  4   17  |
| 1   8   3   | 4   2   7   | 5   9   6   |
| 9   4   27  | 5   1   6   | 28  3   78  |
+-------------+-------------+-------------+
| 8   3   69  | 2   679 4   | 16  17  5   |
| 4   26  5   | 8   67  1   | 3   27  9   |
| 7   1   269 | 3   69  5   | 68  28  4   |
+-------------+-------------+-------------+


So far as I can see, it is a BUG with three 3-candidate cells. Can someone please explain if there is a BUG reduction?

R4C3 is <2>, or R9C3 is <6>, or R7C5 is <6>. Then, what?

Thank you,

Keith

(I already have the Unique UR and the W-wing, thank you.)

How about
r9c5 -6- {r8c5 =6= r8c2 =2= r4c2 -2- r4c3 =2|6= {r7c5, r9c3}} -6- r9c5, => r9c5<>6.

[daj95376]

(I already have the Unique UR and the W-wing, thank you.)

Do you also have the XY-Chain on [r4c2]?

[re'born]

Another way to see that r9c5<>6 is to note that
r9c5=6 => r9c7=8 => r9c8=2
r9c7=8 => r6c7=2
r9c7=8 => r7c7=6.
This gives a reverse BUG pattern on 2 and 6 and hence r9c5<>6.

Similar sorts of arguments show that r4c3=6 will produce a Reverse BUG on 6 and 9 or that r4c2=2 will produce a Reverse BUG on 2 and 9.

[RW]

R4C3 is <2>, or R9C3 is <6>, or R7C5 is <6>. Then, what?

Here's the shortest BUG+3 elimination I can see:
[r7c3](-6-[r9c3])(-6-[r7c5])-6-[r7c7]-1-[r4c7]-2-[r4c3]
=> r7c3<>6

RW

[keith]

Thank you, all, for the responses. Greatly appreciated.

Keith