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 Post subject: CNC KiMo X 3
PostPosted: Wed Nov 27, 2013 4:24 pm 
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Grand Master
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Joined: Wed Apr 30, 2008 9:45 pm
Posts: 694
Location: Saudi Arabia
Consecutive - Non-Consecutive Killer Modulo X 3

This is a KiMo so the 9 cage for example can be 9 or 19.

The dotted cages are non-consecutive and the red cages are consecutive. Order of numbers does not matter (I'm going to try one where it does).

This was hard in the making but when I put in the final lock-down cages it eased off a bit.

It works well but I've had problems getting the difficulty up to assassin level.


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Solution:
351462789
286793154
794581326
543276891
869314275
127859643
632947518
978135462
415628937


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 Post subject: Re: CNC KiMo X 3
PostPosted: Wed Nov 27, 2013 6:26 pm 
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Grand Master
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1894
Location: Lethbridge, Alberta, Canada
HATMAN wrote:
This is a KiMo so the 9 cage for example can be 9 or 19.
I've never come across a KiMo before. I assume from the above statement that the 0 cage can be either 10 or 20 while the 6 cage could be 6 or 16 but, since it's a non-consecutive cage it must be 16.

BTW Is there some reason why the numbers in the vertical KiMo cages aren't in the bottom cells, just like the numbers in the horizontal KiMo cages are in the right-hand cells?


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 Post subject: Re: CNC KiMo X 3
PostPosted: Wed Nov 27, 2013 6:35 pm 
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Grand Master
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Joined: Tue Jun 16, 2009 9:31 pm
Posts: 282
Location: California, out of London
Here's a hint - don't try printing it out and then trying to solve it when it's upside-down :)


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 Post subject: Re: CNC KiMo X 3
PostPosted: Wed Nov 27, 2013 7:21 pm 
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Grand Master
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Joined: Wed Apr 30, 2008 9:45 pm
Posts: 694
Location: Saudi Arabia
Andrew

Yes to the small print.

I came up with the idea of KiMo in 2007 - you can see them on my old website at http://www.diceboard.co.uk.

The reason the number is in the top right cell is so that when printed out you can put 1,2,3 or 4 before it as you solve it.

I gave up on them at udosuk's recommendation as they tend to switch from easy to insanely difficult, with little in between.

With the NC formulation they seem to work.

Wellbeback I'll have a go at it upside down - but I doubt that it will solve.

Just saw the Ireland - All Black match repeated this afternoon as I'd been travelling during it - depressing but wonderful.

Maurice


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 Post subject: Re: CNC KiMo X 3
PostPosted: Wed Nov 27, 2013 7:55 pm 
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Grand Master
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Joined: Wed Apr 30, 2008 9:45 pm
Posts: 694
Location: Saudi Arabia
The upside down one fails on the top three nonets.


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 Post subject: Re: CNC KiMo X 3
PostPosted: Thu Nov 28, 2013 4:37 am 
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Grand Master
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1894
Location: Lethbridge, Alberta, Canada
Two fun puzzles in one day! :D

Loved the way the KiMo 9 cages interact!

Here is my walkthrough for CNC KiMo X 3:
This is a KiMo so the 9 cage for example can be 9 or 19.
The dashed cages (coloured cages on my worksheet) are non-consecutive and the red-border cages consecutive; order of numbers doesn’t matter.

Prelims
KiMo non-consecutive cages
6 KiMo cage must total 16 (cannot be 6 because 1,2,3 are consecutive) = {169/259/268/358}, no 4,7
9 KiMo cages must total 9 or 19 = {135/379/469}, no 2,8
0 KiMo cage must total 10 or 20 = {136/479}, no 2,5,8

1. 9 KiMo cages at R1C9 and R4C9 cannot both total 9 or both total 19 -> one must be {135}, locked for C9, the other must be {469}, locked for C9 -> R9C9 = 7, placed for D\
1a. Naked pair {28} in R78C9, locked for N9

2. R9C9 = 7 -> 9 KiMo cage at R9C7 = {379}, locked for R9 and N9

3. 0 KiMo cage at R3C1 must total 20 = {479} (cannot be {136} which clashes with 9 KiMo cage at R1C1), locked for R3 and N1

4. 9 KiMo cage at R1C1 = {135} (only remaining combination), locked for R1 and N1

5. 9 KiMo cage at R1C9 = {379/469} (cannot be {135} because no 1,3,5 in R1C9), 9 locked for C9 and N3
5a. 9 KiMo cage at R4C9 = {135} (only remaining combination), locked for C9 and N6 -> R3C9 = 6, R12C9 = {49}, locked for C9 and N3

6. 9 KiMo cage at R7C1 = {469} (only remaining combination, cannot be {135} which clashes with R1C1, cannot be {379} because no 3,7,9 in R9C1), locked for C1 and N7 -> R3C1 = 7

7. 9 KiMo cage at R4C3 = {379} (only remaining combination, cannot be {135} which clashes with R1C3, cannot be {469} which clashes with R3C3), locked for C3 and N4 -> R3C3 = 4, placed for D\, R3C2 = 9

8. Non-consecutive cage at R7C3 = {158/258}, 5,8 locked for C3 and N7 -> R1C3 = 1
8a. Non-consecutive cage at R7C3 = {258}, locked for C3 and N7 -> R2C3 = 6, R9C2 = 1
8b. Naked pair {37} in R89C2, locked for C2 -> R1C2 = 5, R1C1 = 3, placed for D\

9. Non-consecutive cage at R4C1 = {158/258}, 5,8 locked for C1 and N4 -> R2C1 = 2, R2C2 = 8, placed for D\

10. 2,9 on D\ only in R4C4 + R5C5 + R6C6, locked for N5

11. Consecutive cage at R4C2 = {123/234/345/456/567}, no 9
11a. 9 in R4 only in R4C78, locked for N6

12. Consecutive cage at R6C7 = {456/567/678}, no 1,2, 6 locked for C7

13. 1 in C7 only in R123C7, locked for N3
13a. Non-consecutive cage at R1C8 = {257/258}, no 3, 2,5 locked for C8 and N3
13b. 5,6 in C7 only in consecutive cage at R6C7 = {456/567}, no 8

14. 9 KiMo cage at R2C4 = {379} (only remaining combination, cannot be {135} which clashes with R2C78, ALS block), locked for R2 and N2 -> R2C7 = 1, R2C8 = 5, placed for D/, R2C9 = 4, R1C9 = 9, placed for D/
14a. R3C7 = 3 (hidden single in N3), placed for D/, R9C78 = [93], R8C2 = 7, placed for D/, R7C2 = 3
14b. R8C2 = 7 -> consecutive cage at R8C1 = {567/789} (cannot be {678} because consecutive cage at R8C7 cannot contain both of 1,2), no 2,4
14c. Naked pair {28} in R7C39, locked for R7

15. Non-consecutive cage at R3C4 = {158} (cannot be {258} which clashes with R3C8), locked for R3 and N2 -> R3C8 = 2

16. Non-consecutive cage at R4C8 = {479} (only remaining cage, cannot be {468/469} which clash with R78C8, ALS block) -> R4C8 = 9, R56C8 = {47}, locked for C8 and N6 -> R1C8 = 8

17. R6C7 = 6, R7C7 = 5, placed for D\

18. R6C6 = 9 (hidden single on D\), R5C3 = 9 (hidden single in R5), R6C2 = 2 (hidden single in R6)

19. Consecutive cage at R4C2 = {234} (only remaining combination) -> R45C2 = [46], R46C3 = [37], R4C4 = 2, R45C7 = [82], R56C8 = [74]

20. R5C5 = 1, placed for D\, R4C6 = 6, R6C4 = 8, both placed for D/, R7C3 = 2, R9C1 = 4

21. Non-consecutive cage at R9C4 = {268} (only remaining combination, cannot be {258} which clashes with R9C3) -> R9C4 = 6, R1C456 = [462], R9C56 = [28]

22. Consecutive cage at R7C5 = {345} (only remaining combination) -> R7C5 = 4, R8C56 = {35}, R8C4 = 1 (hidden single in R8)

and the rest is naked singles, without using the diagonals.

Rating Comment:
I'll rate my walkthrough at Hard 1.0. I used several ALS blocks.


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