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 Post subject: Regular Samurai #15
PostPosted: Mon Aug 04, 2008 9:52 pm 
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There are four difficulties to choose from.
All four puzzles have the same solution.

A) Novice
B) Apprentice (mainstream edition).
C) Master (35 Intersections, 3 Naked Pairs, 4 Naked Triplets, 3 Naked Quads, 1 Hidden Pair, 1 Y-Wing in g3, 2 XY-Chains up to 5 links: one in g1 and one in g3). Select to view GRID numbers.
D) Chief Wizard. Solvable using logic only? JSudoku needs 1 Recursively Solve, which makes 8 guesses and traverses 4232 nodes.



Regular Samurai #15A (Novice)

Rating based on required solving techniques:  Moderate

Image

000900205009030700080100600003018000007000040200000063000000000400020070001609000
003100000050000208000800006000007000001000620000514800000000000000030002008002059
000308000070200000000000008000060002703090005800030000000940000000000000100000000
040005000090000000000000100000502390020008000600010000100000800005760003400000050
000030007000080000000070108000700000000200604900050000002000000005300790600094350



Regular Samurai #15B (Apprentice)

Rating based on required solving techniques:  Barely Hard

Image

000900205009030700080100600003018000007000040200000063000000000400020000001609000
003100000050000208010800006000007000001000620000514800000080000000030002000002059
000308000000200000000000000000060032703090005800030000000940000000000000000000000
000005000090000000000000000000502390020008000600010000100000800005760013400000050
000030007000080000000070108000700000000200604900050000002000000005300790600094350



Regular Samurai #15C (Master)

Rating based on required solving techniques:  Ultra Hard

Image

000900205009030700080100600003018000007000040200000063000000000400020000001609000
003100000050000208010800006000007000001000620000514800000000000000030002000002059
000308000000200000000000000000060032703090005800030000000940000000000000000000000
000005000090000000000000000000502390020008000600010000100000800005760013400000050
000030007000080000000070108000700000000200604900050000002000000005300790600094350



Regular Samurai #15D (Chief Wizard)

Rating based on required solving techniques:  Hellish Nightmare   Solvable using logic only?

Image

000900205009030700080100600003018000007000040200000063000000000400020000001609000
003100000050000208010800006000007000001000620000514800000000000000030002000002059
000308000000200000000000000000060032003090005800030000000940000000000000000000000
000005000090000000000000000000502390020008000600010000100000800005760013400000050
000030007000080000000070108000700000000200604900050000002000000005300790600094350

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 Post subject: Re: Regular Samurai #15
PostPosted: Mon Aug 04, 2008 11:18 pm 
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I can confirm that Chief Wizard #15D is solvable using logic. It does require regional forcing chains, their application in Grid 1 assists JSudoku on solving the puzzle.

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 Post subject: Re: Regular Samurai #15
PostPosted: Tue Aug 05, 2008 8:54 pm 
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Glyn wrote:
It does require regional forcing chains, their application in Grid 1 assists JSudoku on solving the puzzle.
You are absolutely right.

After having JSudoku solve as far as possible, I found the following forcing chain in g1:
(r5c5 = 5)
=> (r1c5 = 6) => (r1c3 = 4)
=> (r5c2 = 1) => (r5c1 = 9) => (r5c9 = 2) => (r4c8 = 5) => (r9c8 = 2) => (r9c7 = 5) => (r9c5 = 4) => (r3c5 = 7)
=> (r1c6 = ?) => (r5c5 = 6)

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 Post subject: Re: Regular Samurai #15
PostPosted: Tue Aug 05, 2008 10:38 pm 
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That move alone isn't enough to crack it.

My first move instead is this Kraken house move. (which you should appreciate being Norwegian)
Code:
(8-37)r9c12=(7)r9c5-(7)r8c46=(7)r8c8
||
(8)r9c5-(8)r1c5=(8)r1c8
||
(8)r9c9
Conclusion r8c8<>8


JSudoku can now advance to this position for Grid 1.

Code:
.------------------.------------------.------------------.
| 1367  1367  46   | 9     678   467  | 2     138   5    |
| 156   256   9    | 2458  3     2456 | 7     18    14   |
| 357   8     245  | 1     457   2457 | 6     39    49   |
:------------------+------------------+------------------:
| 69    46    3    | 245   1     8    | 59    25    7    |
| 159   15    7    | 235   56    2356 | 8     4     129  |
| 2     145   8    | 457   9     457  | 15    6     3    |
:------------------+------------------+------------------:
| 578   2567  256  | 34578 4578  13457| 149   179   169  |
| 4     9     56   | 578   2     157  | 3     17    68   |
| 378   37    1    | 6     478   9    | 45    25    28   |
'------------------'------------------'------------------'


Another Kraken (based on cell r8c4)

Code:
(5)r8c4-(5)r4c4=(5)r4c78-(5=1)r6c7
||
(7)r8c4-(7=1)r8c8
||
(8)r8c4-(8)r8c9=(8-2)r9c9=(2-1)r5c9=(1)r6c7

Common peer of r6c7 and r8c8 => r7c7<>1


Now JSudoku can finish it

It is always best to go for moves that affect the overlap region.

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 Post subject: Re: Regular Samurai #15
PostPosted: Wed Aug 06, 2008 2:49 pm 
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Glyn wrote:
That move alone isn't enough to crack it.
I knew that at the time of posting but forgot to mention it.


Glyn wrote:
It is always best to go for moves that affect the overlap region.
I absolutely agree, but I could not find such a move. :oops:


Glyn wrote:
My first move instead is this Kraken house move. (which you should appreciate being Norwegian)
Code:
(8-37)r9c12=(7)r9c5-(7)r8c46=(7)r8c8
||
(8)r9c5-(8)r1c5=(8)r1c8
||
(8)r9c9
Conclusion r8c8<>8

Another Kraken (based on cell r8c4)
Code:
(5)r8c4-(5)r4c4=(5)r4c78-(5=1)r6c7
||
(7)r8c4-(7=1)r8c8
||
(8)r8c4-(8)r8c9=(8-2)r9c9=(2-1)r5c9=(1)r6c7

Common peer of r6c7 and r8c8 => r7c7<>1
Two excellent Kraken. :salute:
The second one is especially impressive.

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