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HATMAN
 Post subject: Human Solvable 21
PostPosted: Fri Jun 19, 2015 1:15 pm 
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Grand Master
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Joined: Wed Apr 30, 2008 9:45 pm
Posts: 694
Location: Saudi Arabia
Human Solvable 21 Max Repeat Anti-kNight Non-Consecutive

All the cages are 4-cell.
All the cages are maximum repeat i.e. AABB.
It is standard non-consecutive.
It is anti-knight.
The colouring applies to both puzzles which have the same solution.
The second one can be solved without the HS bit.

I'm grateful for any views on difficulty.

HS 21
Image

Image

Non-HS puzzle
Image

Solution:

964137582
137582964
582964137
758296413
413758296
296413758
829641375
641375829
375829641
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wellbeback
 Post subject: Re: Human Solvable 21
PostPosted: Sun Jun 21, 2015 4:19 am 
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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
Ingenious again! here is the HS bit (I assume). Thanks HATMAN!

Rules:
All cages consist of two pairs of numbers.
It is Non-Consecutive and Anti-Knight.

Note that because of the layout of the cages within the grid - the positioning of each pair within each cage can immediately be determined.
Also note that (obviously) each pair add up to half the cage total.
HS Bit:
Call whatever goes in r4c2 = X.

-> r4c3 = (13 - X)
-> r4c4 = 10 - (13 - X) = (X - 3)
-> r5c5 = 7 - (X - 3) = 10 - X
-> r6c6 = 8 - (10 - X) = (X - 2)
-> r6c7 = 10 - (X - 2) = (12 - X)
-> r6c8 = 12 - (12 - X) = X!

i.e., r4c2 = r6c8
-> (Anti-Knight) HS X in n5 -> r5c5 = X
-> X = 10 - X
-> X = 5

-> 26(4)r3c1 = [5858]
-> 20(4)r3c2 = [8282]
-> 14(4)r2c4 = [5225]
-> 16(4)r5c5 = [5335]
-> 20(4)r6c6 = [3737]
-> 24(4)r6c7 = [7575]

Also HP (46) in n5 -> (r4c6,r6c4) = {46}
-> 20(4)r3c5 = [{46}{46}]

Then working out the rest of the solution took me a while. But it was a nicely judged level of difficulty! Just right for the morning coffee. :)
Timing:
Human Solvable bit - 10 mins
Rest of puzzle - 40 mins.
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HATMAN
 Post subject: Re: Human Solvable 21
PostPosted: Sun Jun 21, 2015 4:00 pm 
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Joined: Wed Apr 30, 2008 9:45 pm
Posts: 694
Location: Saudi Arabia
Excellent sir

I did not do it as neatly as you did. I worked out the three possible values in the three cells and that the outer two were equal and pointed to all the cells of N5 except r5c5 and that only five is common to all three.


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Andrew
 Post subject: Re: Human Solvable 21
PostPosted: Fri Jul 03, 2015 10:09 pm 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Thanks HATMAN for another ingenious puzzle! I was impressed by the way wellbeback solved the HS bit! :applause:

I hope that HATMAN won't be disappointed by the way I solved this puzzle. I couldn't see how the extra 24(4) cage at R2C7 could make the difference between this puzzle needing the HS bit so I solved it more conventionally. There were still some interesting steps the way I did it, and I see that I used parts of the HS bit but not all of it. The HS bit is a neat shortcut, but the puzzle isn't particularly difficult without it. And I still don't see what difference that extra 24(4) cage makes.

Here is my walkthrough for Human Solvable 21:
Non-consecutive (NC) horizontally and vertically. All cages have two values both repeated.

Prelims

a) 14(4) repeat cage at R2C4 = 2x{16/25/34}, no 7,8,9
b) 26(4) repeat cage at R3C1 = 2x{49/58} (cannot be 2x{67} because of NC in C2)
c) 20(4) repeat cage at R3C2 = 2x{19/28/37/46}, no 5
d) 20(4) repeat cage at R3C5 = 2x{19/28/37/46}, no 5
e) 24(4) repeat cage at R5C3 = 2x{39/48/57}, no 1,2,6
f) 16(4) repeat cage at R5C5 = 2x{17/26/35}, no 4,8,9
g) 18(4) repeat cage at R5C6 = 2x{18/27/36/45}, no 9
h) 20(4) repeat cage at R6C3 = 2x{19/28/37/46}, no 5
i) 20(4) repeat cage at R6C6 = 2x{19/28/37/46}, no 5
j) 24(4) repeat cage at R6C7 = 2x{39/48/57}, no 1,2,6

Clean-ups resulting from overlapping cages
1a. 5 of 26(4) repeat cage at R3C1 only in R3C1 + R4C2 -> no 8 in R3C1 + R4C2
1b. 1,2,6 of 20(4) repeat cage at R3C2 only in R3C3 + R4C4 -> R3C3 + R4C4 = {126}, no 3,4
1c. 14(4) repeat cage at R2C4 = 2x{16/25} (cannot be 2x{34} because R3C2 + R4C3 only contain 1,2,6), no 3,4
1d. 5 of 14(4) repeat cage at R2C4 only in R2C4 + R5C5 -> no 2 in R2C4 + R5C5
1e. 1,5,6 of 16(4) repeat cage at R5C2 is in R5C5 -> R6C6 + R7C7 = {237}, R8C6 = {156}
1f. 20(4) repeat cage at R6C6 = 2x{28/37} (because R6C6 only contains 2,3,7), no 4,9
1g. 3,7,8 of 24(4) repeat cage at R6C7 in R6C7 + R7C8 -> no 3,7,8 in R6C8 + R7C9

2. 24(4) repeat cage at R5C3 = 2x{39/57} (cannot be 2x{48} which clashes with 26(4) repeat cage at R3C1), no 4,8
2a. Killer pair 5,9 in R4C23 and 24(4) cage, locked for N4
2b. R5C3 + R6C2 = {39/57}, NC no 4,8 in R5C2 + R6C3
2c. R7C3 + R8C4 = {39/57}, NC no 4,8 in R8C3
2d. Clean-up for 20(4) cage at R6C3: no 1,2,6 in R6C4, no 4,8,9 in R7C4, no 1,2,6 in R7C5

3. 18(4) repeat cage at R5C6 = 2x{18/27/45} (cannot be {36} which clashes with R6C6 or R57C6 NC for R6C6), no 3,6

4. 14(4) repeat cage at R2C4 (step 1c) = 2x{16/25}
4a. R2C4 + R3C3 = {16}/[52], CPE/clash no 1,2,5,6 in R2C3 + R3C4
4b. R4C4 + R5C5 = {16}/[25], CPE/clash no 1,2,5,6 in R4C5 + R5C4

5. 16(4) repeat cage at R5C5 = 2x{17/26/35}
5a. R5C5 + R6C6 = [17/53/62], CPE/clash no 2 in R5C6 + R6C5
5b. R7C7 + R8C6 = [26/35/71], CPE/clash no 2 in R7C6 + R8C7
5c. 18(4) repeat cage at R5C6 (step 3) = 2x{18/45}, no 7
5d. Killer pair 1,5 in R4C4 + R5C5 and R5C6 + R6C5, locked for N5
5e. Clean-up for 20(4) cage at R3C5: no 9 in R3C6, no 1 in R3C5, no 9 in R4C7

6. 14(4) repeat cage at R2C4 (step 1c) = 2x{16/25}, 18(4) repeat cage at R5C6 (step 5c) = 2x{18/45}
6a. R5C6 + R6C5 = {18/45}
6b. R4C4 + R5C5 = [25/61] (cannot be [16] which clashes with R5C6 + R6C5 or NC)
6c. Clean-up for 14(4) cage: no 6 in R2C4, no 1 in R3C3
6d. Clean-up for 20(4) cage at R3C2: no 9 in R3C2 + R4C3
6e. Clean-up for 26(4) cage at R3C1: no 4 in R3C1 + R4C2

7. 16(4) repeat cage at R5C5 = 2x{17/35} (cannot be 2x{26} because R5C5 only contains 1,5), no 2,6
7a. Killer pair 1,5 in R57C6 and R8C6, locked for C6
7b. 1 in R3 only in R3C789, locked for N3
7c. Clean-up for 20(4) cage at R3C5: no 9 in R3C5, no 9 in R4C6, no 1 in R4C7

8. 20(4) repeat cage at R6C6 (step 1f) = 2x{37} (cannot be 2x{28} because R6C6 only contains 3,7), no 8
8a. Naked pair {37} in R6C67, locked for R6
8b. Naked pair {37} in R7C78, locked for R7 and N9
8c. Naked pair {37} in R67C7, locked for C7
8d. Naked pair {59} in R46C2, locked for C2 and N4
8e. 24(4) repeat cage at R5C3 (step 2) = 2x{39/57}, R6C2 + R7C3 = {59} -> no 5,9 in R8C4

9. 24(4) repeat cage at R6C7 = 2x{39/57}, no 4
9a. Naked pair {59} in R6C28, locked for R6
9b. Naked pair {59} in R7C39, locked for R7
9c. 20(4) repeat cage at R6C3 = 2x{28/46}, no 1
9d. Naked pair {26} in R36C3, locked for C3
9e. Naked pair {26} in R47C4, locked for C4
9f. Clean-up for 18(4) cage at R5C6: no 4 in R5C6, no 5 in R7C6, no 4 in R8C7

10. 20(4) repeat cage at R3C5 = 2x{28/46} (cannot be {37} because no 3,7 in R4C7), no 3,7
10a. Naked quad {2468} in R3C2356, locked for R3
10b. Naked quad {2468} in R4C3467, locked for R4

11. Killer pair 4,8 in R5C6 + R6C5 and R6C4, locked for N5
11a. Clean-up for 20(4) cage at R3C5: no 2,6 in R3C6, no 4,8 in R3C5, no 2,6 in R4C7
11b. Naked triple {379} in R358C4, locked for C4
11c. Killer pair 4,8 in R3C6 and R57C6, locked for C6

[Only just spotted …]
12. R46C2 = {59} -> no 9 in R5C4 (Anti-Knight)
12a. R3C4 = 9 (hidden single in C4), R4C5 = 9 (hidden single in N5)
12b. R3C1 = 5, R4C2 = 5 -> R3C2 = 8, R4C3 = 8 -> R3C3 = 2, R4C4 = 2 -> R2C4 = 5, R5C5 = 5, R3C567 = [641], R4C67 = [64]
12c. R6C2 = 9 -> R5C3 = 3, R7C3 = 9, R8C4 = 3
12d. R5C5 = 5 -> R6C6 = 3, R7C7 = 3 -> R8C6 = 5
12e. R6C78 = [75], R7C89 = [75], R3C89 = [37], R4C89 = [13]
12f. R6C3 = 6 -> R6C4 = 4, R7C4 = 6, R7C5 = 4
12g. R8C7 = 8 -> R7C6 = 1, R5C6 = 8, R6C5 = 1
12h. R9C4 = 8, R1C4 = 1

[And after those placements, some NCs to give further placements]
13a. R2C4 = 5 -> no 4 in R2C3 -> R12C3 = [47], R12C6 = [72], no 8 in R1C5 -> R12C5 = [38], R1C12 = [96]
13b. R6C19 = [28], R1C9 = 2, R1C7 = 5 -> R2C7 = 9 (cannot be 6, NC)
13c. R6C9 = 8 -> R5C9 = 6 (cannot be 9, NC)
13d. R9C4 = 8 -> R9C5 = 2 (cannot be 7, NC)

and the rest is naked singles.
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