Was Samurai number 19 much more difficult than usual or ...
Posted: Sat Mar 31, 2007 12:55 pm
Was Samurai number 19 much more difficult than usual or did I miss something obvious? At first it seemed easier than usual, and lots of numbers fell into place, but suddenly, I got stuck. I repeatedly went around all the puzzles searching for the usual suspects, XY-wings, hidden pairs, etc., but found nothing.
In then end I found an XY-chain in the bottom right puzzle that established that if there was not an 8 in R3C2 the had to be a 2 in R1C1, and vice versa. Looking at the middle puzzle, this meant that there was either an 8 in R9C8 or a 2 in R7C7. A 2 in R7C7 implies a 6 in R3C7 and an 8 in R9C8 means a 3 in R6C8, an 8 in R6C9 and a 5 in R1C9. So, using an XY-chain that spanned two puzzles I can see that if there is not a 6 in R3C7 there is a 5 in R1C9 and vice versa. If there is a 5 in R1C9 there is only one cell left in the box for an 8, R1C7. So, there must either be an 8 in R1C7 or a 6 in R3C7. But if there is an 8 in R1C7 there is only one cell left in the box for a 6, R3C7. So there must either be a 6 in R3C7 or a 6 in R3C7 Then the rest of the puzzles quickly fell into place.
At the top of the Samurai Contest page Ruud has written, “These can be solved with singles, line-box interactions, naked and hidden subsets and an occasional X-wing.” So I think I must have missed something simple. Could anyone point it out for me please?
Here is where I got to with each of the puzzles:
Top Left:
.------------------.------------------.------------------.
| 8 247 1 | 3 247 6 | 479 5 479 |
| 6 2347 24 | 5 247 9 | 1478 13478 13478|
| 9 347 5 | 47 1 8 | 2 3467 3467 |
:------------------+------------------+------------------:
| 457 1 6 | 2 478 3 | 478 9 4578 |
| 3 8 24 | 147 9 5 | 6 1247 147 |
| 457 245 9 | 6 478 147 | 3 12478 14578|
:------------------+------------------+------------------:
| 15 9 7 | 8 6 12 | 145 13 1234 |
| 145 45 8 | 179 3 127 | 1579 167 12679|
| 2 6 3 | 1479 5 147 | 1789 178 1789 |
'------------------'------------------'------------------'
Top Right:
.------------------------.------------------------.------------------------.
| 1 345 6 | 58 9 358 | 7 2 34 |
| 23459 23459 7 | 125 6 1235 | 358 158 134 |
| 235 8 235 | 4 7 1235 | 356 156 9 |
:------------------------+------------------------+------------------------:
| 2345789 2345679 23589 | 25789 238 25789 | 1 89 67 |
| 23789 2379 1 | 6 238 2789 | 89 4 5 |
| 5789 5679 589 | 5789 1 4 | 2 3 67 |
:------------------------+------------------------+------------------------:
| 5678 157 58 | 1279 4 1279 | 3569 1569 123 |
| 357 1579 359 | 12789 28 6 | 4 159 12 |
| 26 129 4 | 3 5 19 | 69 7 8 |
'------------------------'------------------------'------------------------'
Middle:
.------------------.------------------.------------------.
| 145 13 1234 | 12 67 9 | 5678 157 58 |
| 1579 167 12679| 12 4 8 | 357 1579 359 |
| 1789 178 1789 | 3 67 5 | 26 129 4 |
:------------------+------------------+------------------:
| 17 5 17 | 6 8 3 | 9 4 2 |
| 38 2 38 | 4 9 1 | 57 6 57 |
| 46 9 46 | 7 5 2 | 1 38 38 |
:------------------+------------------+------------------:
| 69 67 79 | 8 3 4 | 25 25 1 |
| 13 138 138 | 5 2 6 | 4 79 79 |
| 2 4 5 | 9 1 7 | 38 38 6 |
'------------------'------------------'------------------'
Bottom Left:
.---------------.---------------.---------------.
| 5 2 8 | 3 4 1 | 69 67 79 |
| 7 4 9 | 2 6 5 | 13 138 138 |
| 6 1 3 | 7 8 9 | 2 4 5 |
:---------------+---------------+---------------:
| 2 8 1 | 9 5 7 | 346 36 34 |
| 4 3 5 | 6 12 8 | 19 127 1279|
| 9 7 6 | 4 12 3 | 5 128 128 |
:---------------+---------------+---------------:
| 1 9 24 | 8 7 6 | 34 5 234 |
| 3 6 7 | 5 9 24 | 8 12 124 |
| 8 5 24 | 1 3 24 | 7 9 6 |
'---------------'---------------'---------------'
Bottom Right:
.---------------.---------------.---------------.
| 25 25 1 | 3 8 4 | 7 6 9 |
| 4 79 79 | 5 1 6 | 2 3 8 |
| 38 38 6 | 2 7 9 | 4 5 1 |
:---------------+---------------+---------------:
| 379 379 5 | 1 39 8 | 6 2 4 |
| 1 23 4 | 6 35 25 | 8 9 7 |
| 289 6 289 | 47 49 27 | 3 1 5 |
:---------------+---------------+---------------:
| 578 4578 3 | 9 6 57 | 1 478 2 |
| 6 2457 27 | 8 245 1 | 9 47 3 |
| 2789 1 2789| 47 24 3 | 5 478 6 |
'---------------'---------------'---------------'
Thanks,
Brian.
In then end I found an XY-chain in the bottom right puzzle that established that if there was not an 8 in R3C2 the had to be a 2 in R1C1, and vice versa. Looking at the middle puzzle, this meant that there was either an 8 in R9C8 or a 2 in R7C7. A 2 in R7C7 implies a 6 in R3C7 and an 8 in R9C8 means a 3 in R6C8, an 8 in R6C9 and a 5 in R1C9. So, using an XY-chain that spanned two puzzles I can see that if there is not a 6 in R3C7 there is a 5 in R1C9 and vice versa. If there is a 5 in R1C9 there is only one cell left in the box for an 8, R1C7. So, there must either be an 8 in R1C7 or a 6 in R3C7. But if there is an 8 in R1C7 there is only one cell left in the box for a 6, R3C7. So there must either be a 6 in R3C7 or a 6 in R3C7 Then the rest of the puzzles quickly fell into place.
At the top of the Samurai Contest page Ruud has written, “These can be solved with singles, line-box interactions, naked and hidden subsets and an occasional X-wing.” So I think I must have missed something simple. Could anyone point it out for me please?
Here is where I got to with each of the puzzles:
Top Left:
.------------------.------------------.------------------.
| 8 247 1 | 3 247 6 | 479 5 479 |
| 6 2347 24 | 5 247 9 | 1478 13478 13478|
| 9 347 5 | 47 1 8 | 2 3467 3467 |
:------------------+------------------+------------------:
| 457 1 6 | 2 478 3 | 478 9 4578 |
| 3 8 24 | 147 9 5 | 6 1247 147 |
| 457 245 9 | 6 478 147 | 3 12478 14578|
:------------------+------------------+------------------:
| 15 9 7 | 8 6 12 | 145 13 1234 |
| 145 45 8 | 179 3 127 | 1579 167 12679|
| 2 6 3 | 1479 5 147 | 1789 178 1789 |
'------------------'------------------'------------------'
Top Right:
.------------------------.------------------------.------------------------.
| 1 345 6 | 58 9 358 | 7 2 34 |
| 23459 23459 7 | 125 6 1235 | 358 158 134 |
| 235 8 235 | 4 7 1235 | 356 156 9 |
:------------------------+------------------------+------------------------:
| 2345789 2345679 23589 | 25789 238 25789 | 1 89 67 |
| 23789 2379 1 | 6 238 2789 | 89 4 5 |
| 5789 5679 589 | 5789 1 4 | 2 3 67 |
:------------------------+------------------------+------------------------:
| 5678 157 58 | 1279 4 1279 | 3569 1569 123 |
| 357 1579 359 | 12789 28 6 | 4 159 12 |
| 26 129 4 | 3 5 19 | 69 7 8 |
'------------------------'------------------------'------------------------'
Middle:
.------------------.------------------.------------------.
| 145 13 1234 | 12 67 9 | 5678 157 58 |
| 1579 167 12679| 12 4 8 | 357 1579 359 |
| 1789 178 1789 | 3 67 5 | 26 129 4 |
:------------------+------------------+------------------:
| 17 5 17 | 6 8 3 | 9 4 2 |
| 38 2 38 | 4 9 1 | 57 6 57 |
| 46 9 46 | 7 5 2 | 1 38 38 |
:------------------+------------------+------------------:
| 69 67 79 | 8 3 4 | 25 25 1 |
| 13 138 138 | 5 2 6 | 4 79 79 |
| 2 4 5 | 9 1 7 | 38 38 6 |
'------------------'------------------'------------------'
Bottom Left:
.---------------.---------------.---------------.
| 5 2 8 | 3 4 1 | 69 67 79 |
| 7 4 9 | 2 6 5 | 13 138 138 |
| 6 1 3 | 7 8 9 | 2 4 5 |
:---------------+---------------+---------------:
| 2 8 1 | 9 5 7 | 346 36 34 |
| 4 3 5 | 6 12 8 | 19 127 1279|
| 9 7 6 | 4 12 3 | 5 128 128 |
:---------------+---------------+---------------:
| 1 9 24 | 8 7 6 | 34 5 234 |
| 3 6 7 | 5 9 24 | 8 12 124 |
| 8 5 24 | 1 3 24 | 7 9 6 |
'---------------'---------------'---------------'
Bottom Right:
.---------------.---------------.---------------.
| 25 25 1 | 3 8 4 | 7 6 9 |
| 4 79 79 | 5 1 6 | 2 3 8 |
| 38 38 6 | 2 7 9 | 4 5 1 |
:---------------+---------------+---------------:
| 379 379 5 | 1 39 8 | 6 2 4 |
| 1 23 4 | 6 35 25 | 8 9 7 |
| 289 6 289 | 47 49 27 | 3 1 5 |
:---------------+---------------+---------------:
| 578 4578 3 | 9 6 57 | 1 478 2 |
| 6 2457 27 | 8 245 1 | 9 47 3 |
| 2789 1 2789| 47 24 3 | 5 478 6 |
'---------------'---------------'---------------'
Thanks,
Brian.