The New Sudoku Players' Forum

Website · by **denis_berthier** » Thu Feb 09, 2023 7:18 am

.

Code: Select all: +-------+-------+-------+ ! 1 . 3 ! . 5 6 ! . . . ! ! . . 7 ! 1 8 . ! . . . ! ! 8 . . ! 3 . 7 ! 1 . . ! +-------+-------+-------+ ! . 3 6 ! 5 . 8 ! . 1 7 ! ! 5 1 . ! 7 . . ! . . 3 ! ! 7 . 8 ! . . . ! . . . ! +-------+-------+-------+ ! . . . ! 8 . . ! 6 9 . ! ! 6 . 5 ! . . . ! . . . ! ! . . . ! . . . ! . 4 . ! +-------+-------+-------+ 1.3.56.....718....8..3.71...365.8.1751.7....37.8.........8..69.6.5.............4.;67;559 SER = 11.6

Code: Select all: Resolution state after Singles (and whips[1]-: +----------------------+----------------------+----------------------+ ! 1 249 3 ! 249 5 6 ! 24789 278 2489 ! ! 249 24569 7 ! 1 8 249 ! 23459 2356 24569 ! ! 8 24569 249 ! 3 249 7 ! 1 256 24569 ! +----------------------+----------------------+----------------------+ ! 249 3 6 ! 5 249 8 ! 249 1 7 ! ! 5 1 249 ! 7 2469 249 ! 2489 268 3 ! ! 7 249 8 ! 2469 123469 12349 ! 2459 256 24569 ! +----------------------+----------------------+----------------------+ ! 234 247 124 ! 8 12347 12345 ! 6 9 125 ! ! 6 24789 5 ! 249 123479 12349 ! 2378 2378 128 ! ! 239 2789 129 ! 269 123679 12359 ! 23578 4 1258 ! +----------------------+----------------------+----------------------+ 203 candidates.

by **Cenoman** » Thu Feb 09, 2023 3:44 pm

This one may be solved with help of RT:

Code: Select all: +----------------------+--------------------------+-------------------------+ | 1 249* 3 | 249* 5 6 | 24789 278 2489 | | 249* 56 7 | 1 8 249* | 23459 2356 24569 | | 8 56 249* | 3 249* 7 | 1 256 24569 | +----------------------+--------------------------+-------------------------+ | 249* 3 6 | 5 249* 8 | 249 1 7 | | 5 1 249* | 7 2469 249* | 2489 268 3 | | 7 249* 8 | 249+6* 13 13 | 2459 256 24569 | +----------------------+--------------------------+-------------------------+ | 234 247 124 | 8 12347 12345 | 6 9 125 | | 6 24789 5 | 249 123479 12349 | 2378 2378 128 | | 239 2789 129 | 269 123679 12359 | 23578 4 1258 | +----------------------+--------------------------+-------------------------+

TH(249)b1245 having a single guardian => +6 r6c4; lcls, 5 placements
Note RT(249) at r1c24, r6c2

Code: Select all: +----------------------+----------------------+----------------------+ | 1 249* 3 | 249* 5 6 | 7-249 78 2489 | | 249 56 7 | 1 8 249 | 2459 3 24569 | | 8 56 249 | 3 249 7 | 1 25 24569 | +----------------------+----------------------+----------------------+ | 249 3 6 | 5 249 8 | x249* 1 7 | | 5 1 249 | 7 249 249 | 8 6 3 | | 7 x249* 8 | 6 13 13 | X2459 X25 X2459 | +----------------------+----------------------+----------------------+ | 234 247 124 | 8 137 12345 | 6 9 125 | | 6 24789 5 | 249 137 12349 | 237 78 128 | | 239 2789 129 | 29 6 12359 | 2357 4 1258 | +----------------------+----------------------+----------------------+

ER(2,4,9) at b6 => xr6c2 is also true at r4c7 => RT(249) r1c24, r4c6 => -249 r1c7; lcls, 8 placements

Code: Select all: +--------------------+-------------------+----------------------+ | 1 249 3 | 49 5 6 | 7 8 249 | | 249 56 7 | 1 8 249 | 2459 3 24569 | | 8 56 249 | 3 249 7 | 1 25 24569 | +--------------------+-------------------+----------------------+ | 249 3 6 | 5 249 8 | 249 1 7 | | 5 1 249 | 7 249 249 | 8 6 3 | | 7 249 8 | 6 13 13 | 2459 25 2459 | +--------------------+-------------------+----------------------+ | 234 24 124 | 8 7 135 | 6 9 15 | | 6 8 5 | 49 13 49 | 23 7 12 | | 39 7 19 | 2 6 135 | 35 4 8 | +--------------------+-------------------+----------------------+

The puzzle is then solved with five simple AICs
3. (2)r1c2 = r1c9 - r3c8 = r6c8 => -2 r6c2
4. (5)r9c6 = (5-3)r7c6 = r7c1 - (3=91)r9c13 => -1 r9c6; 3 placements
5. (2)r5c6 = r2c6 - r2c1 = r4c1 => -2 r5c3; 2 placements
6. (9)r3c3 = r5c3 - r5c56 = r4c5 => -9 r3c5
7. (9=2)r3c3 - r1c2 = (2-4)r1c9 = (4)r3c9 => -9 r3c9; ste

by **eleven** » Thu Feb 09, 2023 10:46 pm

Same 2 steps at the beginning.
Here from the RT 2 numbers directly follow:

Code: Select all: +--------------------+-------------------+----------------------+ | 1 *249 3 | *49 5 6 | 7 8 249 | | 249 56 7 | 1 8 249 | 2459 3 24569 | | 8 56 249 | 3 249 7 | 1 25 24569 | +--------------------+-------------------+----------------------+ | 249 3 6 | 5 249 8 | 249 1 7 | | 5 1 249 | 7 249 249 | 8 6 3 | | 7 *249 8 | 6 13 13 | 2459 25 2459 | +--------------------+-------------------+----------------------+ | 234 4-2 124 | 8 7 135 | 6 9 15 | | 6 8 5 | 49 13 49 | 23 7 12 | | 39 7 19 | 2 6 135 | 35 4 8 | +--------------------+-------------------+----------------------+

r7c2 can't be 2 (must be in the RT), and 4r7c2 implies 4r1c4.

Code: Select all: *------------------------------------------------------------* | 1 29 3 | 4 5 6 | 7 8 29 | | 24-9 56 7 | 1 8 *29 | 2459 3 24569 | | 8 56 *249 | 3 2-9 7 | 1 25 24569 | |-------------------+-----------------+----------------------| | 249 3 6 | 5 249 8 | 29 1 7 | | 5 1 *249 | 7 249 *29 | 8 6 3 | | 7 29 8 | 6 13 13 | 2459 25 2459 | |-------------------+-----------------+----------------------| | 23 4 2-1 | 8 7 135 | 6 9 a15 | | 6 8 5 | 9 13 4 | 23 7 12 | | b39 7 b19 | 2 6 135 | b35 4 8 | *------------------------------------------------------------*

(1=5)r7c9 - (5=391)r9c713 => -1r7c3
Then (1r9c3) skyscraper 9 c36 => -9r3c5,r1c2, stte

Website · by **denis_berthier** » Sat Feb 11, 2023 4:18 am

.
Thanks for your solutions.
Indeed, I had intended this as an example of using the 630 impossible patterns. I forgot that RT is often available when the basic tridagon elimination rule is at work.
I'll propose another example.

The New Sudoku Players' Forum

#155 in 63137 T&E(3) min-expands

#155 in 63137 T&E(3) min-expands

Re: #155 in 63137 T&E(3) min-expands

Re: #155 in 63137 T&E(3) min-expands

Re: #155 in 63137 T&E(3) min-expands