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 Post subject: Star Battle Killer
PostPosted: Fri Nov 25, 2016 2:48 am 
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Here's a puzzle I posted to the Daily League yesterday

Place the numbers 1-8 and two stars in each row, column, and jigsaw group. Stars cannot touch each other, even diagonally. Numbers cannot repeat within cages. Stars count as 0 in cages.

Image

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 Post subject: Re: Star Battle Killer
PostPosted: Tue Nov 29, 2016 4:35 pm 
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Location: California, out of London
Hi h3lix. One question. Can stars repeat in cages? Thanks - wellbeback.

Update: Never mind. I see the answer is yes. The 3(4) cage requires two stars!


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 Post subject: Re: Star Battle Killer
PostPosted: Wed Nov 30, 2016 6:40 pm 
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That's correct. Cages can have any number of stars.

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 Post subject: Re: Star Battle Killer
PostPosted: Thu Dec 01, 2016 5:35 am 
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Grand Master
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Location: Saudi Arabia
Pleasant puzzle H3lix and a beautiful example.

I tried it a couple of times on paper and kept making mistakes - so I loaded it into JSudoku where it does not solve. If you remember back with Mike Japan's 007 puzzles we occasionally had this.

The reason is that JC's coding has two separate zeros say 0 and 0'. If you consider your 3(4) it must have 1,2, 0 and 0'. Whereas LOL on r12345 means r6c2 (6/8) = r5c6 (7/8) and r5c9 (0/0'/1/2) = r6c7 (0/0'/1/2). r5c9 and r6c7 are both in 3(4) so must be 0 0 or 0' 0'.

Hence the conflict - but not on paper.

Cheers

Maurice


Last edited by HATMAN on Mon Dec 05, 2016 12:54 pm, edited 1 time in total.

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 Post subject: Re: Star Battle Killer
PostPosted: Thu Dec 01, 2016 10:36 pm 
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Thanks Maurice! I was having trouble getting JSudoku to generate a star battle solution in the first place, since as you mentioned JC's code handles duplicate values as different numbers and FNC, NC, and AK concurrently in a Latin Square grid produces no solution. I had to manually grab all the 9's from a solution, put it into a new grid, remove all A candidates from cells surrounding 9's, turn on anti-king, and hope there was a solution. 9 times out of 10 there wasn't.

I just now tried a different approach: Set a 10x10 Latin Square grid with the values 0,1,3,5,7,9,B,D,F,H, turn on NC, FNC, and AK, and voila, the 0's and 1's in a generated grid form a star battle solution! I just hope that somehow AK on the other values doesn't limit the possible number of solutions that can be generated.

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 Post subject: Re: Star Battle Killer
PostPosted: Mon Dec 05, 2016 12:06 am 
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Thanks h3lix for an interesting and enjoyable puzzle. I also took several tries, for the reasons given in my walkthrough, but after that when I re-worked it, the puzzle was fairly easy.

Here is my walkthrough for Start Battle Killer:
This is a jigsaw killer. Each row, column and jigsaw group contains 1-8 and two *s, which count as zero. Stars cannot touch horizontally, vertically or diagonally.

Since there are 10 rows and columns, I’ve labelled them 1-9 and A; CA is the right-hand column, RA is the bottom row. Jigsaw groups are identified by their upper-left cells, for example JR1C5.

On my earlier attempts, after doing the 3(4) cage I’d forgotten about stars not touching so I started again and have made a point of emphasising this feature.

Prelims

a) 7(3) cage at R1C2, no 8
b) 8(4) cage at R1C2, no 8
c) 8(2) cage at R1CA, no 4, can only have one *
d) 9(2) cage at R2C7, no *
e) 2(2) cage at R3C3 = {2*}
f) 10(2) cage at R3C4, no 1,5,*
g) 10(2) cage at R4CA, no 1,5,*
h) 7(2) cage at R5C2, no 8, can only have one *
i) 6(2) cage at R5C4, no 7,8, can only have one *
j) 3(4) cage at R5C9 = {12**}
k) 7(2) cage at R6C1, no 8, can only have one *
l) 14(2) cage at R6C2 = {68}
m) 7(2) cage at R6C4, no 8, can only have one *
n) 14(2) cage at R9C1 = {68}
o) 3(3) cage at R9C7, no 4,5,6,7,8
p) 3(3) cage at RAC4, no 4,5,6,7,8

1a. Naked pair {2*} in 2(2) cage at R3C3, 2 and one * locked for C3 and JR2C2; at this stage 7(2) cage at R5C2 retains one *
1b. Naked pair {68} in 14(2) cage at R6C2, locked for R6
1c. Naked pair {68} in 14(2) cage at R9C1, locked for R9 and JR6C1
1d. Naked pair {68} in R69C2, locked for C2
1e. Naked pair {68} in 14(2) cage at R6C2, CPE no 6,8 in R25C3
1f. 10(2) cage at R3C4 = {37/46}, no 8
1g. 7(2) cage at R5C2 = {7*} (cannot be {34} which clashes with 10(2) cage), 7 and one * locked for R5 and JR2C2, clean-up: no 3 in R4CA
1h. 10(2) cage = {46}, locked for R3 and JR2C2 -> R6C2 = 8, R6C3 = 6, 14(2) cage at R9C1 = [86], clean-up: no 3,5 in R2C7
1i. 7(2) cage at R6C1 = {25/34/7*}, no 1
1j. 7(2) cage at R6C4 = {25/34/7*}, no 1
1k. R2C23 = {135} (no stars) -> 9(3) cage at R2C1 = {135}, locked for R2, clean-up: no 3,5,7 in R1CA, no 8 in R3C7
[I tend to only use Law of Leftovers (LoL) for harder jigsaws and jigsaw killers. However since HATMAN posted a comment about using LoL, it could be used after step 1 for C123, R12C4 + 10(2) cage at R3C4 must exactly equal R678C3 + R8C2, 10(2) cage = {46} -> no 4,6 in R12C4, R78C3 + R8C2 must contain 4, locked for JR6C3.]

2. 3(4) cage at R5C9 = {12**}, * cannot be touching even diagonally -> R5C9 = *, R6C7 = *, R6C89 = {12}, locked for R6 and JR5C9, no *s in cells touching R5C9 and R6C7, clean-up: no 5 in R7C1, no 5 in R7C4
2a. 7(2) cage at R5C2 = {7*}, R5C9 = * -> no other * in R5
2b. 11(3) cage at R7C7 = {38*/47*/56*) -> R7C78 = {38/47/56}, R7C9 = *
2c. R57C9 = {**}, locked for C9 and JR5C9
2d. 6(2) cage at R5C4 = {15/24}, no 3,6

3. 36 rule on JR1C7 + JR2C7, 1 innie R6C7 = * -> 2 outies R45C6 = 15 = [78], clean-up: no 2 in R4CA, no 3 in R5CA
[or as HATMAN pointed out R5C6 = R6C2 from LoL R12345]
3a. R45C6 = 15 -> R45C7 = 6 = {15/24}/[*6], no 3, no 6 in R4C7
3b. 8(2) cage at R1CA = [17/8*/*8] (cannot be {26} which clashes with 10(2) cage at R4CA), no 2,6
3c. 36 rule on JR5C9 1 innie R8C8 = 1 outie R9CA + 7 -> R8C8 = {78}, R9CA = {1*}
3d. 3(3) cage at R9C7 + R9CA = 3(4)/4(4) = {12**/13**}, no other 1 or * in R9 and JR8C7
3e. 36 rule on CA 2 innies R30CA = 3 = [12/*3]
3f. Naked quint {123**} in R9C7890 + RACA, locked for JR8C7
3g. 16(3) cage at R8C7 = {457} -> R8C8 = 7, R8C79 = {45}, locked for R8 and JR8C7
3h. R8C8 = 7 -> R9CA = *
3i. R7C78 = {38/56), no 4
3j. 4 in JR6C9 only in 15(4) cage at R6CA, locked for CA -> 10(2) cage at R4CA = [82], 8(2) cage at R1CA = [17], R3CA = *, R9CA = *, RACA = 3, R8CA = 6, clean-up: no 2 in R3C7
3k. 3(3) cage at R9C7 = {12*}, 2 locked for R9
3l. 3(3) cage at RAC4 = {12*}, 1,2 and one * locked for RA and JR5C6
3m. Naked triple {678} in RAC789, 7 locked for RA
3n. Naked triple {45*} in RAC123, locked for JR6C1 -> 7(2) cage at R6C1 = {7*}, locked for JR6C1, R9C3 = 3
3o. R7C2 + R8C1 = {12} (hidden pair in JR6C1), CPE no 1,2 in R8C2
3p. R7C78 = {38}, locked for R7, clean-up: no 4 in R6C4

4. R7C6 = 6 (hidden single in JR5C6) -> R6C56 = 8 = {35}, locked for R6 and JR5C6, R8C6 = *, no *s in touching cells, R9C456 = [574]
4a. 6(2) cage at R5C4 = [15], R6C56 = [35], R67CA = [45]
4b. 7(2) cage at R6C4 = {7*}, 7 and one * locked for C4 and JR6C3

5. R2C4 = 8 (hidden single in JR1C1), clean-up: no 1 in R3C7
5a. R1C5 = 8 (hidden single in JR1C5)
5b. R8C3 = 8 (hidden single in JR6C3)
5c. R7C235 = {124} (hidden triple in R7), no *

6. 7 in R1 only in 7(3) cage at R1C2 = [*7*], two *s locked for R1 and JR1C1, no * in R2C5
6a. 7(2) cage at R5C2 = [7*] -> 2(2) cage at R3C3 = [*2], 7(2) cage at R6C1 = [*7], 7(2) cage at R6C4 = [7*], no * in R8C4
6b. R8C24 = [*3] (hidden pair in JR6C3)
6c. 15(5) cage at R3C1 = {12345} (only combination because no *s), no 6
6d. R1C1 = 6 (hidden single in C1)
6e. Naked triple {345} in R1C789, locked for R1 and JR1C7 -> R2C89 = [*6], no * in R3C8, clean-up: no 3 in R3C7
6f. R2C6 = * (other * in R2)
6g. R9C8 = * (other * in C8)
6h. R28C6 = {**}, locked for C6
6i. R13C6 = [23] -> R2C5 = 4, 9(2) cage at R2C7 = [27], 10(2) cage at R3C4 = [46]
6j. Naked pair {12} in R78C5, locked for C5 and JR6C3 -> 3(3) cage at RAC4 = [2*1], R4C45 = [6*]
6k. R3C1 = 2 (hidden single in JR1C1), R8C1 = 1, R7C2 = 2, R78C5 = [12]
6l. Naked triple {345} in R245C1, locked for C1 and JR1C1 -> R234C2 = [351], RAC123 = [*45]

7. R4C7 = * (second * in JR2C7) -> R5C7 = 6 (cage sum), RAC789 = [867], R7C78 = [38]
7a. 3(3) cage at R9C7 = [1*2] -> R6C89 = [21]
7b. R3C8 = 1, R2C8 = * -> R1C78 = 7 = [43]

and the rest is naked singles, without using jigsaw groups or *s.

Solution:
6 * 7 * 8 2 4 3 5 1
5 3 1 8 4 * 2 * 6 7
2 5 * 4 6 3 7 1 8 *
4 1 2 6 * 7 * 5 3 8
3 7 * 1 5 8 6 4 * 2
* 8 6 7 3 5 * 2 1 4
7 2 4 * 1 6 3 8 * 5
1 * 8 3 2 * 5 7 4 6
8 6 3 5 7 4 1 * 2 *
* 4 5 2 * 1 8 6 7 3


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