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About that number 4...

 
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Ruud
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Joined: 30 Dec 2005
Posts: 601

PostPosted: Fri Nov 02, 2007 11:02 pm    Post subject: About that number 4... Reply with quote

Here is the fullfillment of the number 4 prophecy.



SumoCueV1=18J0+0J0+0J0=18J0+3J1=22J1+5J1=14J1+7J1+0J0=45J0+3J0+3J0+10J2+5J1=15J1+10J1+7J3=15J4=16J4+19J0=21J5=12J2+22J2+15J1+15J3=8J3+18J4+18J4=20J6+21J5+21J5+22J2=24J2+33J2+26J3=18J4+10J6+29J6+21J5+10J5=20J5+33J2+10J2+26J3+36J4+29J6+29J6=8J6+41J5+41J5+33J2=18J3+52J3+36J4=9J4+55J7+48J6+48J6+41J5=13J8+60J3+52J3=18J4+10J7+55J7=14J7+10J6=19J8+68J8+10J8=20J8+63J7+63J7+66J7+66J7+68J7+68J8+71J8+71J8+71J8

The blue cells can be seen as a center-dot group or a size-9 cage as shown in the picture.

Number 4 is jumping right at you. The other numbers are not so forthcoming...

Enjoy,
Ruud

PS: It has (4+4) cages of size 4. This would have been TJK32. (4+4)x4=32. pale
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Caida
Hooked
Hooked


Joined: 03 Nov 2007
Posts: 38
Location: Canada

PostPosted: Sun Nov 04, 2007 12:02 am    Post subject: walkthrough for number 4 Reply with quote

Hello,

Here is my walkthrough for this jigsaw killer. I found this one quite easy. I have struggled with all others and have been unable to solve the latest one (Texas Jigsaw Killer 032 - July 18, 2007).

As this is my first time doing a walkthrough I am not sure if I have the notations quite right. Any comments/suggestions would be most appreciated. (also first time posting - so not even sure if I am doing this right)


Caida

edited to fix formating/notational errors based on what I've learned so far


Firstly Nonets are as follows
n1 @ r1c1
n2 @ r1c5
n3 @ r2c5
n4 @ r2c9
n5 @ r3c1
n6 @ r3c4
n7 @ r4c3
n8 @ r7c3
n9 @ r7c7
nX special 45 rule at r2c258+r5c258+r8c258

Prelims:
a. 9(3)n58 = {126/135/234} (no 7..9)
b. 8(3)n4 and n7 = {125/134} (no 6..9) (1 locked for n4c9 and for n5)
c. 22(3)n2 = {589/679} (no 1..4) (9 locked for n2)
d. 16(2)n51 = {79} (no 1..6,8) (7,9 locked for r3)
e. 13(2)n94 = {49/58/67} (no 1..3)


1. Innie n6: r5c5 = 4
1a. 4 locked for nX

2. Innies n7: r5c2+r8c5 = 17(2) {89} (no 1..7)
2a. {89} locked for n7 and for NX

3. Innies n3: r2c5+r5c8 = 9(2) = {27/36} (no 1,5)

4. 20(4)n7 = {2567/3467} and 16(2)n51 = {79} (prelim d); both require 7
4a. since both are only in c23 then no 7 anywhere else in c23

5. Innies n5: r37c2+r1c8 = 12(3) = [7]{14}/[7]/{23}/[9]({12}
5a. r7c2 and r8c1 no (5..9)

6. 18(3)n58 = {189/279/369/378/459/468}
6a. if r3c2 = 9 then r4c2 = 8 (step 2) and r8c1 = {1/2} this requires 7 or 8 or 9 in r9c2, doesn’t work
6b. -> r3c23 = [79]
6c. clean up (most using LOL):
6c1. r3c7 no 1
6c2. r2c59, r7c7 no 7
6c3. r2c6 no 9; r2c9 = 9; r567c6 no 9
6c4. r7c8 no 6
6c5. r7c7 no 4
6c6. r5c8 no 2

7. 14(3)n24 = [149]/{23}[9]
7a. r1c89 no (5..8)
7b. r1c8 no 4
7c. cleanups (most using LOL)
7c1. r3c7 no 4
7c2. r3c7 r7c37 no 5
7c3. r7c37 no 6
7c4. r3c7 no 8
7c5. r7c8 no 7,8

8. 12345 locked for r7c23458

9. 9(3)n58 = {12}[6]/{13}[5]/{234}
9a. r8c3 no 1

10. killer pair {45} locked for n4 in 8(3) and r7c8

11. 18(3)n4 = {279/369/378}
11a. killer pair {23} locked for n4 in 18(3) and 8(3)

12. 15(3)n24 = [726]/{186}/[528]
12a. killer pair {12} for n2 in r1c89 and r23c7
12b. no 2 in r1c5
12c. r2c7 no 234
12d. r3c7 no 3
12e. r1c9 = 4; r1c8 = 1
12f. r2c7 no 6,8
12g. r3c7 = 2

13. 8(3)n4 = {125} locked for n4c9
13a. r7c8 = 4
13b. r7c7 = 9
13c. r2c5 = 2 (LOL)
13d. r5c8 = 7 (step 3) (2,7 locked for nX)

14. 18(3)n4 = [873]
14a. r1c6 and r4c8 = 9
14b. r3c8 = 6; r2c7 = 7

15. 22(9) = {589} locked for n2
15a. r2c8 = 3
15b. r1c5 = 6
15c. r8c8 = 5
15d. r9c8 = 2

16. 20(4)n9 = {4268}
16a. r9c7 = 4
16b. cleanup: r8c5 = 9 (LOL)
16c. r5c2 = 8 (step 2)
16d. r5c4, r6c1, r9c2 = 9

17. 19(4)n89 = {1378}
17a. r9c5 = 8
17b. r9c9 = 6
17d. r8c9 = 8

18. 8(3)n7 = {125} (must contain 5) this locks 5 in n7 and 2 in c4
19. {16} locked in nX and c2
19a. r6c2 = 4
19b. {367} locked in r456c3

20. 18(3)n58 = [279]
20a. cleanup: r7c2 = 3
20b. r8c3 = 4
20c. r4c2 = 5
20d. r1c2 = 2
20e. r7c3 = 2

21. 18(3)n5 = [198]

everything else become just clean up of singles


Last edited by Caida on Tue Dec 11, 2007 3:48 am; edited 1 time in total
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mhparker
Grandmaster
Grandmaster


Joined: 20 Jan 2007
Posts: 345
Location: Germany

PostPosted: Thu Nov 08, 2007 12:38 pm    Post subject: "About That Number 4" Walkthrough Reply with quote

Hi folks,

Thought I'd join Caida and Gary in doing this puzzle (Note: Gary's solving outline can be found here).

Caida found an early move that I missed. I've added a note about that immediately after my step 6.

It's interesting to note that...

Select text in box (e.g., by triple-clicking it) to see what I wrote:
...both Caida and Gary used basically the same hypothetical to get into the puzzle (Gary's step 4 and Caida's step 6a). I missed that, so ended up (instead) having to use the R2 innies to eliminate the {168} combo for the 15(3) cage at R2C7, and hence work out the mappings between R2C59 and R3C37 (LoL R12).


Note that this time I used the "8(3) at R3C9" notation, rather than the "8(3)n4" notation I sometimes use. There's no particular reason for that, and both forms are of course valid.

Many thanks to Ruud for once again providing an interesting and enjoyable jigsaw killer. Roll on TJK33!


"About That Number 4" Walkthrough

Nonet Layout:

111122222
111132224
551633244
557663334
577666334
577766344
558776944
588879999
888889999

Prelims

a) 22(3) at R1C6 = {589/679} (no 1..4); 9 locked for N2
b) 16(2) at R3C2 = {79}, locked for R3; no 7,9 in R12C2 (CPE)
c) 8(3) at R3C9 = {125/134} (no 6..9); 1 locked for C9 and N4
d) 8(3) at R6C4 = {125/134} (no 6..9); 1 locked for N7
e) 9(3) at R7C2 = {126/135/234} (no 7..9)
f) 13(2) at R7C7 = {49/58/67} (no 1..3)

1. Innie N6: R5C5 = 4

2. Innies N7: R5C2+R8C5 = 17(2) = {89}, locked for N7 and 45(9) at R258C258

3. LoL R89: R7C37 = R8C15
3a. {89} unavailable in R7C3 -> R8C5 = R7C7 and hence R8C1 = R7C3
3a. -> R7C7 = {89}, no 7..9 in R8C1
3b. cleanup: R7C8 = {45}; no 1,2 in R9C12

4. R7C8 and 8(3) at R3C9 form killer pair (KP) on {45} -> no 4,5 elsewhere in N4

5. Innies N4: R2C9+R37C8 = 19(3) = {469/478/568} (no 2,3) (other combos unplaceable)

6. Innies N3: R2C5+R5C8 = 9(2) = {27/36} (no 1,5) (other combos unplaceable)

--- Note: missed grouped X-Wing (well-)spotted by Caida here: ---
--- 7 in N7 and 16(2) at R3C2 locked in C23 -> not elsewhere in C23 ---

7. 14(3) at R1C8: min R2C9 = 6 -> max. R1C89 = 8
7a. -> no 8 in R1C89
7b. 1 unavailable in R1C9
7c. -> no 6,7 in R1C8

8. Both of {89} in N2 locked in R1C567+R2C67+R3C7
8a. LoL C89: R1C567+R2C67+R3C7 (6 outies) = R4589C8+R89C9 (6 innies)
8b. -> R4589C8+R89C9 must also contain both of {89}
8c. R89C89 cannot contain both of {89} due to R7C7
8d. -> R4C8 = {89} (only other place available)
8e. other of {89} must go in R8C9+R9C89
8f. -> R7C7 and R89C89 form KP on {89} -> no 8,9 elsewhere in N9 (R89C67)

9. Innies N5: R37C2+R8C1 = 12(3) = {129/147/237} (no 5,6) (other combos unplaceable)
9a. cleanup: no 3,4 in R9C12
9b. no 5,6 in R7C3 (step 3)

10. Hidden quad at R7C1679 = {6789} (no 1..5)

11. 9(3) at R7C2: max. R7C23 = 7 -> min. R8C3 = 2
11a. -> no 1 in R8C3

12. LoL C12345: R123C5 (3 innies) = R567C6 (3 outies)
12a. no 9 in innies
12b. -> no 9 in outies

13. LoL C123: R4C3+R56C23 (5 innies) = R1289C4+R9C5 (5 outies)
13a. no 1 in innies
13b. -> no 1 in outies

14. 18(3) at R5C1 = {189/369/378/459/468/567} (no 2)
(Note: {279} blocked by R3C2)

15. LoL R12: R2C59 (2 innies) = R3C37 (2 outies)
15a. none of {145} in innies
15b. -> no 1,4,5 in R3C7

16. 15(3) at R2C7 = {168/258/267/348} (other combos unplaceable)
16a. must have exactly 1 of {1457}, only available in R2C7
16b. -> R2C7 = {1457} (no 2,3,6,8)

17. Innies R12: R2C2578 = 18(4) = {1467/2367/2457/3456} (other combos unplaceable)
17a. 4 only available in R2C7
17b. -> no 1,5 in R2C7
17c. 15(3) at R2C7 = [438/726]
17d. -> no 6,8 in R3C7

18. LoL R12 (step 15): {23} unavailable in R2C9
18a. -> R3C7 = R2C5, and (hence) R3C3 = R2C9
18b. -> R2C5 = {23} (no 6,7); R2C9 = {79} (no 6,8)
18c. cleanup: no 2,3 in R5C8 (step 6); no 7 in R1C9

--- Note: puzzle cracked now: rest is basically just mop-up ---

19. Innies N4 (step 5) = [784/964] (only possible permutations)
19a. -> R7C8 = 4
19b. -> R7C7 = 9
19c. -> R8C5 = 9 (step 3)
19d. -> R5C2 = 8 (step 2)
19e. cleanup: no 2,3 in R8C3, no 4 in R8C1 (step 3)

20. 8(3) at R3C9 = {125} (no 3) (last combo), locked for C9 and N4

21. 9 in C9 locked in N4 -> not elsewhere in N4 (R6C8)

22. Hidden single (HS) in C8 at R4C8 = 9

23. HS in N6 at R5C4 = 9

24. 5 in R7 locked in 8(3) at R6C4 = {125} (no 3,4), locked for N7
24a. no 5 in R6C4

25. 18(3) at R6C8 = {369/378} (other combos unplaceable)
25a. 6 of {369} must go in R7C9
25b. -> no 6 in R6C89
25c. 3 locked in R6C89 for R6

26. 3 in N7 locked in C3 -> not elsewhere in C3

27. HS in R7 at R7C2 = 3
27a. cleanup: no 6 in R8C3

28. 8 in N5 locked in C1 -> not elsewhere in C1

29. 18(3) at R8C1 = {279} (last combo)
29a. -> R8C1 = 2
29b. R9C12 = {79} (no 5,6), locked for R9 and N8
29c. R7C3 = 2 (step 3)
29d. -> R8C3 = 4 (cage sum)

30. R6C24 = [42] (hidden singles, N7)

31. LoL C123: R1267C4+R78C5 (6 outies) = R7C3+R8C23+R9C123 (6 innies)
31a. outies contain naked pair (NP) = {15}
31b. -> innies must contain both of {15}, only available at R8C2+R9C3
31c. -> R8C2+R9C3 = {15} (no 6,8), locked for N8
31d. innies contain 4 and 7 (from NP on {79} at R9C12)
31e. -> R12C4 = {47} (no 3,5,6,8), locked for C4, N1 and 18(4) cage

32. R3C23 = [79]
32a. -> R2C9 = 9 (step 15)
32b. -> R3C8 = 6 (step 19)

33. Naked single (NS) at R5C8 = 7
33a. -> R2C5 = 2 (step 6)
33b. -> R2C7 = 7 (cage sum), R3C7 = 2 (step 15)

And the rest is singles and cage sums.

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Mike
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