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 Post subject: U-N-Killer 1
PostPosted: Tue Feb 07, 2023 8:16 am 
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Grand Master
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Joined: Wed Apr 30, 2008 9:45 pm
Posts: 694
Location: Saudi Arabia
U-N-Killer 1

Standard Killer, but the numbers are from 0 to 9 and one of them is not used anywhere, so you have to find the missing number.

Image

For those of you that use JSudoku, I attach a zip file with the base layout and this puzzle.

Not too hard
Maurice


Attachments:
U-N-Killer.zip [4.42 KiB]
Downloaded 222 times


Last edited by HATMAN on Sat Mar 18, 2023 6:34 pm, edited 1 time in total.
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 Post subject: Re: U-N-Killer 1
PostPosted: Tue Feb 07, 2023 8:24 am 
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Grand Master
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Joined: Wed Apr 30, 2008 9:45 pm
Posts: 694
Location: Saudi Arabia
If some of you try this the next variant is "zero is everywhere, but each of the other nine numbers is absent from just one nonet, row and column".
Finding solutions will be the first problem.


Last edited by HATMAN on Tue Feb 07, 2023 11:26 am, edited 1 time in total.

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 Post subject: Re: U-N-Killer 1
PostPosted: Tue Feb 07, 2023 11:25 am 
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Grand Master
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Joined: Wed Apr 30, 2008 9:45 pm
Posts: 694
Location: Saudi Arabia
Actually it was not that difficult I just remembered some of the patterns that I used to play with:

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 Post subject: Re: U-N-Killer 1
PostPosted: Thu Apr 06, 2023 3:48 am 
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Grand Master
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
"Not too hard" but interesting enough to have been posted and for me to post my walkthrough. Steps 4 and 5 were my key steps.

Here's how I solved U-N-Killer 1:
Uses the numbers 0-9, one of which is missing which is part of the puzzle.

Prelims

a) R1C67 = {69/78}
b) R23C3 = {49/58/67}
c) R34C1 = {79}
d) R45C2 = {49/58/67}
e) R67C7 = {79}
f) 7(3) cage at R1C1 = {016/025/034/124}
g) 7(3) cage at R1C4 = {016/025/034/124}
h) 7(3) cage at R2C6 = {016/025/034/124}
i) 7(3) cage at R2C8 = {016/025/034/124}
j) 4(3) cage at R5C5 = {013}
k) 7(3) cage at R5C7 = {016/025/034/124}
l) 7(3) cage at R6C1 = {016/025/034/124}
m) 7(3) cage at R6C2 = {016/025/034/124}
n) 7(3) cage at R7C8 = {016/025/034/124}
o) 7(3) cage at R8C3 = {016/025/034/124}
p) 7(3) cage at R9C5 = {016/025/034/124}

1a. Naked pair {79} in R34C1, locked for C1
1b. Naked pair {79} in R67C7, locked for C7, clean-up: no 6,8 in R1C6
1c. Naked triple {013} in 4(3) cage at R5C5, locked for N5
1d. 7(3) cage at R6C2 = {025/124} (cannot be {016/034} which clash with 4(3) cage), no 3,6, 2 locked for R6
1e. 3 of 4(3) cage must be in R6C56 (which cannot be {01} which clashes with 7(3) cage), 3 locked for R6
1f. Killer pair 0,1 in 7(3) cage and R6C56, locked for R6
1g. R6C1 = {456} -> no 4,5,6 in R7C12
1h. 7(3) cage at R5C7 = {025/034/124} (cannot be {016} which clashes with R5C5), no 6
1i. Killer pair 0,1 in R5C5 and 7(3) cage, locked for R5
[At this stage 0,1,2,3,7,9 are in all rows, columns and nonets.]

2a. 17(3) cage at R4C4 = {269/278/458/467}
2b. Hidden killer pair 7,9 in 17(3) cage and R5C4 must each contain one of 7,9 for N5 -> 17(3) cage = {269/278/467} (cannot be {458}), no 5, R5C4 = {79}
2c. Hidden killer pair 0,1 in R4C3 and 7(3) cage at R6C2 for N4, 7(3) cage (step 1d) contains one of 1,2 -> R4C3 = {01}
2d. R4C3 = {01} -> R5C34 = {79}/[89], 9 locked for R5, clean-up: no 4 in R4C2
2e. Killer triple 7,8,9 in R4C1, R45C2 and R5C3, locked for N4
[8 must also be used in all rows, columns and nonets since 7,8,9 are required for R4C1, R45C2 and R5C3.]
2f. 8 in C1 only in R89C1, locked for N7
2g. 17(3) cage at R7C4 = {089/269/278/359/368/458/467} (cannot be {179} which clashes with R7C7), no 1
2h. R6C789 = {789} (hidden triple in R6), locked for N6
2i. 8 in C7 only in R123C7, locked for N3
2j. R168C8 = {789} (hidden triple in C8)
2k. Naked pair {79} in R1C68, locked for R1

3a. R5C1 = 3 (hidden single in N4)
3b. 7(3) cage at R5C7 (step 1h) = {025/124}, 2 locked for R5 and N6
3c. 2 in R4 only in R4C456, locked for N5
3d. 7(3) cage at R6C2 (step 1d) = {025/124}
3e. R6C4 = {45} -> no 4,5 in R6C23

4a. If 6 is one of the numbers used then 6 in N6 only in R4C789, locked for R4 or if 6 is missing then no 6 in R4 -> either way no 6 in R4C2456, clean-up: no 7 in R5C2
4b. Cannot have all of 4,5,6 in N5
4c. 17(3) cage at R4C4 (step 2b) = {269/278/467}
4d. Consider placements for R6C4 = {45}
R6C4 = 4 => 17(3) cage = {269/278}
or R6C5 = 5 => 17(3) cage cannot contain both of 4,6
-> 17(3) cage = {269/278}, no 4, 2 locked for N5
4e. Naked pair {45} in R4C6 + R6C4 -> N5 cannot also contain 6 so 6 is the missing number, clean-up: no 7 in R23C3, no 7 in R4C2
4f. 17(3) cage = {278}, 7 locked for N5 -> R5C4 = 9

5a. If R23C3 and R45C2 both have the same combination then R89C1 must also have that combination but there’s no 9 in R89C1 -> at least one of R23C3 and R45C2 must be {58} -> CPE no 5,8 in R123C2
5b. R1C7 = 8 -> R1C6 = 7, R5C36 = [78], R4C3 = 1 (cage sum), R34C1 = [79], R4C2 = 8 (hidden single in N4) -> R5C2 = 5, R6C1 = 4, R6C4 = 5, R4C6 = 4
5c. 8 in N1 only in R23C3 = {58} -> R3C2 = 9 (hidden single in N1) -> R23C5 = [98] (hidden pair in N2), R23C3 = [85], R2C9 = 7 (hidden single in N3)

6a. Naked pair {02} in R6C23, 0 locked for R6 -> R5C5 = 0 (hidden single in N5)
6b. R4C6 = 4 -> R23C6 = {03/12}
6c. Killer pair 1,3 in R23C6 and R6C6, locked for C6
6d. R1C5 = 5 (hidden single in N2)
6e. 4 in N2 only in R123C4, locked for C4
6f. 7(3) cage at R2C8 = {025/034} (cannot be {124} which clashes with R5C8), no 1, 0 locked for C8
6g. 7(3) cage at R7C8 = {025/034} (cannot be {124} because naked triple {124} in R579C8 clashes with 7(3) cage at R2C8) -> R8C7 = 0, R79C8 = {25/34}
6h. R5C8 = 1 (hidden single in C8)
6i. 7(3) cage at R8C3 = {124} (only remaining combination), locked for R8, 1 locked for N8
6j. 7(3) cage at R1C4 contains 4 for N2 = {034} (cannot be {124} which clashes with R8C4), 0,3 locked for C4 and N2

7a. R89C1 = {58} (hidden pair in C1)
7b. 17(3) cage at R8C2 = {278/359} (cannot be {089} because R8C2 only contains 3,7, cannot be {179} because R9C1 only contains 5,8, cannot be {458} because 5,8 only in R9C1) -> R9C3 = {29}
7c. Variable hidden killer pair 7,8 in 17(3) cage at R7C4 and R9C4 for N8, R9C4 cannot contain more than one of 7,8 -> 17(3) cage (step 2g) = {458} (cannot be {089} because 0,9 only in R7C6, cannot be {278} which clashes with R9C4) = [845]
7d. Naked pair {12} in R8C45, 2 locked for R8 and N8
7e. R9C56 = [30] -> R9C7 = 4 (cage sum)
7f. R79C8 = 7 = [25]
7g. R9C1 = 8 -> R8C2 + R9C3 = 9 = [72], R9C2 = 1, R7C1 = 0
7h. R12C1 = {12} -> R2C2 = 4 (cage sum)

and the rest is naked singles.

Solution:
1 0 3 4 5 7 8 9 2
2 4 8 0 9 1 5 3 7
7 9 5 3 8 2 1 4 0
9 8 1 2 7 4 3 0 5
3 5 7 9 0 8 2 1 4
4 2 0 5 1 3 9 7 8
0 3 9 8 4 5 7 2 1
5 7 4 1 2 9 0 8 3
8 1 2 7 3 0 4 5 9


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