Walkthrough for fdkr045a puzzle (courtesy of udosuk):

Innies @ r3: r3c5=5, Outies @ r89: r7c5=1
=> r1c5+r2c34567=28-5=23={123467}, r89c5=10-1=9={27|36}
16/2 @ r5c12={79} (NP @ r5,n4) => 9/2 @ r5c89={18|36|45}
Innies @ n5: r5c456=11 => r5c37=45-16-9-11=9={18|36|45}
=> 2 @ r5,n5,45/9 locked @ r5c456={2(18|36|45)}
=> 2 @ r4 locked @ r4c1289 i.e. one of the two 8/2 cages
=> 6 @ r4 locked @ r4c1289={(17|35)26} has 3|7

Innies @ r4: r4c37=10=[19] (cannot be [37])
=> 19/3 @ r4c456={478} (NT @ r4,n5)
=> HS @ c5: r46c5=[89] => r6c46=15-9=6={15} (NP @ r6,n5)
=> r5c456={236} (NT @ r5,45/9)
=> Outies @ r45: r6c37=15=[87]
=> r5c37={45} (NP @ r5) => r5c89={18}
=> 4 @ c5,n2,28/7 locked @ r12c5

9/2 @ r1c34={27|36}, 14/2 @ r1c67=[68|86|95]
13/2 @ r12c1={49|58|67}, 12/2 @ r12c9={39|48|57}
9/2 @ r12c8={27|36|45} ({18} conflicts r5c8)
=> HS @ r1: 10/2 @ r12c2=[19] => r5c12=[97]
=> 5 @ n1 locked @ r12c1={58} (NP @ c1,n1)
=> r1c1 & r1c67 form complex NP {58} @ r1
=> r12c8=[27|36|45|63|72], r12c9=[48|75|93]
=> HS @ r2: r2c5=4 => 4 @ r1,n3 locked @ r1c89
=> either r2c8=9-4=5 or r2c9=12-4=8 => r2c9 cannot be 5
=> r12c9=[48|93] has 4|9 => 13/2 @ r67c9=[67]

6/2 @ r67c1={24} (NP @ c1) => 6 @ r4,n4 locked @ r4c12=[62]
=> r67c1=[42] => r5c37=[54], r6c28=[32]
=> r12c8=[36|45|63] => HS @ c8,n3: r3c18=[37]
=> 4 @ r3 locked @ r3c234=21-3=18={468}
=> r3c4=8, r3c23={46} (NP @ r3,n1) => r1c34={27} (NP @ r1)
=> r89c5={27} (NP @ c5,n8) ({36} conflicts r1c5)

9 @ c6,n2 locked @ r13c6, 9 @ c9,n3 locked @ r13c9
28/5 @ r89 from {12345689} must contain a 9 => r8c8=9
r7c678=18-2=16 from {34568} must be {358} (NT @ r7)
r12c8 & r4c8 form complex NP {35} @ c8
=> r7c8=8 => r5c89=[18] => r12c9=[93]
=> r1c67=[68], r12c8=[45] => r9c8=6
=> r8c679+r9c6=28-9=19 from {123458} must be {2458}
=> HS @ r8: r89c1=[17] => r9c23=15-7=8=[53]

All naked singles from here.