Walkthrough of Puzzle 31 courtesy of udosuk.

I decide to write a walkthrough for this one because while it doesn't require many advanced tricks, the solving route is quite narrow... It could take ages before you hit the right spot and crack it open... This type of puzzles seems to be more enjoyable to players, compared to those INSANE/RUUDICULOUS ones which require branching/hypothesis/half-T&E moves to solve... Smile

If you want to see the original puzzle, just find any of Frank's posts, click the "www" button underneath and visit his site... There're 32 puzzles for now (with solutions too), many of which have been posted here already... (Alternatively, perhaps Frank would like to post the pic here himself... Wink)

If you haven't done that already, I recommend you to go and try the puzzle out before you read my walkthrough and compare our ways...

Enough babbling... Here it is:

Complete walkthrough for fdkr031:

Innies @ n8 => r7c456=11
Innies @ r7 => r7c19=16={79} (NP @ r7)
13/2 @ r7c78={58} (NP @ r7/n9), 8/2 @ r9c78={17|26}
=> 7/2 @ r8c78 cannot be {16}, must be {34} (NP @ r8/n9)
Innies @ n9 => r789c9=17={9(17|26)} with 9 locked
=> 9 eliminated from r1..6c9, r6c8

Outies @ n9 => r6c89=10={28|37|46}
Outies @ n3 => r4c89=7={16|25|34}
Innies @ c789 => r46c7=7={16|25} ({34} conflicts r8c7)
=> 9 @ n6 locked in 21/3 @ r5c789={(48|57)9}
One of r4c89 and r46c7 must contain a 1, i.e. {16}
=> r6c89={28|37} => 27/5 @ c89={(18|36)279}
=> {27} eliminated from r45c9 => r4c8<>5

5/2 @ r3c78={14|23}, 9/2 @ r12c7={18|27|36|45}
=> 9 @ n3 locked in 15/2 @ r12c8={69} (NP @ c8/n3)
=> r5c7=9 (HS @ c7/n6), r5c89=[48|75|84]
=> r7c78=[85] (HS @ c8 ) => 9/2 @ r12c7={27|45}
=> r46c7 cannot be {25}, must be {16} (NP @ c7/n6)
=> r9c78=[71], r7c19=[79], r12c7={45} (NP @ c7/n3)
=> r8c78=[34], r3c78=[23], r4c89=[25], r5c89=[84]
=> r6c89=[73], r89c9={26}, r123c9={178}

15/2 @ r89c2={69} (NP @ c2/n7)
=> 7/2 @ r89c3={25} (NP @ c3/n7)
=> 5/2 @ r7c23={14} (NP @ r7/n7) => r89c1=[83]
r6c12=25-7-8-3=7={25} ({16} conflicts r6c7) (NP @ r6/n4)
=> 14/3 @ r5c123={167} (NT @ r5/n4)

Innies @ n1 => r123c1=17={269} (NT @ c1/n1)
=> r4c1=4, r5c123=[176], r6c12=[52]
=> r4c2=29-2-6-9-4=8, r46c3=[39]
=> 7/2 @ r2c23=[34], 12/2 @ r3c23=[57], 9/2 @ r1c23=[18]
=> r12c7=[45], r1c9=7, r7c23=[41], r7c456={236} (NT @ n8 )

20/3 @ n8 cannot have 1 => r8c4=1 (HS @ n8 )
=> r67c4=16-9=7=[43], 7/2 @ r67c5=[16]
=> r46c7=[16], r67c6=[82], 13/2 @ r34c5=[49]
=> 8/3 @ n2={125}, r1c6=5, r2c56=[21]

All naked singles remain...

Mr. Green