While learning the Killer lingo and techniques, I tried this Times Killer from time to time, but I could not crack it.

Jean-Christophe's way to solve it seemed to difficult for a published puzzle. My aim was to find a path that does not require me to 'remember' the temporary results of various '45' tests.

Here is an alternative way that I finally managed to find:

Start with the easy pickings:

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`45 on N3: Outie 4 in r4c9`

45 on N7: r7c23=5, r7c3=4, r7c2=1. r6c3=9.

r789c1 = {689} locked

Check configurations and identify mandatory digits in cages.

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`Cage 19/3 in N4 = {478|568}. 8 is locked in r45c2.`

Cage 22/3 in N69 = {589|679}. 9 is locked in r7c89.

Cage 10/2 in N9 = {28|37}. Eliminate {16}

6 is locked in r7c789. r7c1=8.

cage 25/4 in N8 cannot be {4678}.

cage 25/4 requires 9. Locked in r8c56. r8c1 = 6. r9c1 = 9.

These are the key steps:

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`45 on N8: r56c4 + r9c7 = 22/3 = {589|679}. r5c4=9.`

Cage 10/2 in N8 cannot be {19}. r9c8 = 1.

N9: Cage 8/3 = {1}+{25|34}, 10/2 = {28|37}. {23} locked in 2 cages. r7c7 <> {23}

From here on, it is fairly simple.

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`{23} locked in r7+N8`

r9c45 = {46} locked

r9c67 = {57} locked. r9c9=8. r8c9=2.

r8c23 = {57} locked

r8c78 = {34} locked

Cage 25/4 requires 8. r8c56 = {89} locked. r8c4=1. r6c4=8. r7c4=2.

Cage 25/4 = {3589}. r7c56 = {35} locked. r7c7=6. r9c6=7. r9c7=5.

r7c89 = {79} locked. r6c8=6.

r6c67 = {12} locked

r6c12 = {34} locked

cage 13/2 in N5 = {67} r6c5=7. r5c5=6. r6c9=5. r5c6=4. r9c5=4. r9c4=6.

cage 19/3 in N4 = {568} => r4c2=6. r5c1=5. r5c2=8.

cage 16/4 in N45 = {1357}.

r45c3 = {17} locked. r8c3=5. r8c2=7. r4c1=2.

r4c45 = {35} locked. r4c6=1. r6c6=2. r6c7=1. r4c3=7. r5c3=1.

cage 15/3 in N3 = {249|348}. {4} locked in r123c7. r8c7=3. r8c8=4.

cage 15/3 in N3 = {249}. {9} locked in r123c7. r4c7=8. r4c8=9. r3c6=3.

r5c7=7. r5c9=3. r5c8=2. r7c8=7. r7c9=9. r7c6=5. r7c5=3.

r4c5=5. r4c4=3.

r3c89 = {56}. r3c8=5. r3c9=6. r3c3=8.

r3c12 = {19}. r3c1=1. r3c2=9. r3c5=2. r3c7=4. r3c4=7. r2c5=1. r2c4=5. r1c4=4.

r2c23 = {36}.

all singles from here.

This has been a great learning exercise!

Ruud.