The New Sudoku Players' Forum

[International_DBA]

Here is a 6x6 puzzle:
https://andrewspuzzles.blogspot.com/202 ... -by-6.html

[denis_berthier]

Here is a 6x6 puzzle:
https://andrewspuzzles.blogspot.com/202 ... -by-6.html

It's an easy one, solvable by whips[2]:

Hidden Text: Show

(solve Hidato geometric 6 36
. 17 . . 11 13
. . 16 . . .
. 36 . 31 . .
35 . . . 7 .
. . 1 2 . .
. . . . . . )
***********************************************************************************************
*** HidatoRules 2.1.s based on CSP-Rules 2.1.s, config = W+S
*** using CLIPS 6.32-r764
***********************************************************************************************
undecided numbers: (3 4 5 6 8 9 10 12 14 15 18 19 20 21 22 23 24 25 26 27 28 29 30 32 33 34)
singles: r2c5 = 14, r2c6 = 12
296 candidates, 4283 csp-links and 12095 links. Density = 27.7%
whip[1]: r6c1{n26 .} ==> r6c6 ≠ 26, r1c1 ≠ 24, r1c1 ≠ 25, r1c3 ≠ 24, r1c3 ≠ 25, r1c4 ≠ 24, r1c4 ≠ 25, r2c1 ≠ 25, r2c2 ≠ 25, r2c4 ≠ 25, r3c5 ≠ 25, r3c6 ≠ 24, r3c6 ≠ 25, r4c6 ≠ 24, r4c6 ≠ 25, r5c5 ≠ 25, r5c6 ≠ 24, r5c6 ≠ 25, r6c5 ≠ 25, r6c6 ≠ 24, r6c6 ≠ 25, r1c1 ≠ 26, r1c3 ≠ 26, r1c4 ≠ 26, r3c6 ≠ 26, r4c6 ≠ 26, r5c6 ≠ 26
whip[1]: n3{r6c5 .} ==> r3c6 ≠ 4
whip[1]: n6{r5c6 .} ==> r6c3 ≠ 5
whip[1]: n5{r6c6 .} ==> r6c2 ≠ 4
whip[1]: n30{r4c4 .} ==> r5c6 ≠ 29
whip[1]: n20{r4c4 .} ==> r5c6 ≠ 21
whip[1]: n10{r2c4 .} ==> r3c6 ≠ 9
hidden-pairs: {n10 n15}{r1c4 r2c4} ==> r2c4 ≠ 32, r2c4 ≠ 30, r2c4 ≠ 29, r2c4 ≠ 28, r2c4 ≠ 27, r2c4 ≠ 26, r2c4 ≠ 24, r2c4 ≠ 23, r2c4 ≠ 22, r2c4 ≠ 21, r2c4 ≠ 20, r2c4 ≠ 19, r2c4 ≠ 9, r2c4 ≠ 5, r1c4 ≠ 29, r1c4 ≠ 28, r1c4 ≠ 27, r1c4 ≠ 23, r1c4 ≠ 22, r1c4 ≠ 21, r1c4 ≠ 20, r1c4 ≠ 19
whip[1]: n19{r3c3 .} ==> r3c5 ≠ 20, r3c6 ≠ 21, r4c6 ≠ 21
whip[1]: n9{r3c5 .} ==> r1c4 ≠ 10, r3c5 ≠ 8
singles: r2c4 = 10, r1c4 = 15
whip[1]: n30{r4c4 .} ==> r1c3 ≠ 29
whip[2]: r6c1{n27 n22} - r1c1{n18 .} ==> r6c6 ≠ 27, r3c5 ≠ 26, r5c5 ≠ 26, r6c5 ≠ 26, r1c3 ≠ 27, r3c6 ≠ 27, r4c6 ≠ 27, r5c6 ≠ 27
whip[2]: n27{r6c5 r2c2} - n29{r3c5 .} ==> r1c3 ≠ 28
whip[1]: r1c3{n23 .} ==> r5c1 ≠ 21, r5c2 ≠ 21, r5c5 ≠ 21, r6c1 ≠ 22, r6c2 ≠ 22, r6c3 ≠ 22, r6c4 ≠ 22, r6c5 ≠ 22, r6c6 ≠ 22
whip[1]: r6c2{n28 .} ==> r1c1 ≠ 27, r2c1 ≠ 26, r2c2 ≠ 26
whip[1]: n21{r4c4 .} ==> r5c6 ≠ 22
whip[2]: r1c1{n23 n28} - r6c1{n24 .} ==> r3c5 ≠ 21, r3c6 ≠ 22, r4c6 ≠ 22
whip[2]: n22{r5c5 r2c2} - n20{r2c2 .} ==> r1c3 ≠ 21
whip[2]: n21{r4c4 r2c2} - n19{r2c2 .} ==> r1c3 ≠ 20
whip[2]: n20{r4c4 r2c2} - n18{r2c2 .} ==> r1c3 ≠ 19
whip[2]: r1c3{n23 n18} - r1c1{n19 .} ==> r6c1 ≠ 24, r6c2 ≠ 24, r6c3 ≠ 24, r6c4 ≠ 24, r6c5 ≠ 24
whip[2]: n22{r5c2 r5c5} - n24{r5c5 .} ==> r6c6 ≠ 23, r5c6 ≠ 23, r6c4 ≠ 23, r6c5 ≠ 23
whip[2]: n23{r6c3 r2c2} - n21{r2c2 .} ==> r1c3 ≠ 22
whip[2]: n22{r5c5 r2c2} - n24{r3c5 .} ==> r1c3 ≠ 23
S+W1 tte
20 17 18 15 11 13
21 19 16 10 14 12
22 36 32 31 9 8
35 23 33 30 7 6
24 34 1 2 29 5
25 26 27 28 3 4

For fun, just to test the z-chains in another context than Sudoku, I also solved it with z-chains[2], which makes it still easier.

Hidden Text: Show

undecided numbers: (3 4 5 6 8 9 10 12 14 15 18 19 20 21 22 23 24 25 26 27 28 29 30 32 33 34)
start solution 1.118887
entering BRT
singles: r2c5 = 14, r2c6 = 12
296 candidates, 4283 csp-links and 12095 links. Density = 27.7%
whip[1]: r6c1{n28 .} ==> r6c6 ≠ 26, r1c1 ≠ 24, r1c1 ≠ 25, r1c1 ≠ 26, r1c3 ≠ 24, r1c3 ≠ 25, r1c3 ≠ 26, r1c4 ≠ 24, r1c4 ≠ 25, r1c4 ≠ 26, r2c1 ≠ 25, r2c2 ≠ 25, r2c4 ≠ 25, r3c5 ≠ 25, r3c6 ≠ 24, r3c6 ≠ 25, r3c6 ≠ 26, r4c6 ≠ 24, r4c6 ≠ 25, r4c6 ≠ 26, r5c5 ≠ 25, r5c6 ≠ 24, r5c6 ≠ 25, r5c6 ≠ 26, r6c5 ≠ 25, r6c6 ≠ 24, r6c6 ≠ 25
whip[1]: n3{r6c5 .} ==> r3c6 ≠ 4
whip[1]: n6{r5c6 .} ==> r6c3 ≠ 5
whip[1]: n5{r5c6 .} ==> r6c2 ≠ 4
whip[1]: n30{r4c4 .} ==> r5c6 ≠ 29
whip[1]: n20{r4c4 .} ==> r5c6 ≠ 21
whip[1]: n10{r2c4 .} ==> r3c6 ≠ 9
hidden-pairs: {n10 n15}{r1c4 r2c4} ==> r2c4 ≠ 32, r2c4 ≠ 30, r2c4 ≠ 29, r2c4 ≠ 28, r2c4 ≠ 27, r2c4 ≠ 26, r2c4 ≠ 24, r2c4 ≠ 23, r2c4 ≠ 22, r2c4 ≠ 21, r2c4 ≠ 20, r2c4 ≠ 19, r2c4 ≠ 9, r2c4 ≠ 5, r1c4 ≠ 29, r1c4 ≠ 28, r1c4 ≠ 27, r1c4 ≠ 23, r1c4 ≠ 22, r1c4 ≠ 21, r1c4 ≠ 20, r1c4 ≠ 19
whip[1]: n19{r1c3 .} ==> r3c5 ≠ 20, r3c6 ≠ 21, r4c6 ≠ 21
whip[1]: n9{r3c5 .} ==> r3c5 ≠ 8, r1c4 ≠ 10
hidden-single: r2c4 = 10
hidden-single: r1c4 = 15
whip[1]: n30{r4c4 .} ==> r1c3 ≠ 29
z-chain[2]: n27{r6c6 r2c2} - n29{r2c2 .} ==> r1c3 ≠ 28
z-chain[2]: n28{r1c1 r2c2} - n26{r2c2 .} ==> r1c3 ≠ 27
whip[1]: r1c3{n23 .} ==> r5c1 ≠ 21, r5c2 ≠ 21, r5c5 ≠ 21, r6c1 ≠ 22, r6c2 ≠ 22, r6c3 ≠ 22, r6c4 ≠ 22, r6c5 ≠ 22, r6c6 ≠ 22
whip[1]: r6c2{n28 .} ==> r1c1 ≠ 27, r2c1 ≠ 26, r2c2 ≠ 26
whip[1]: r6c1{n28 .} ==> r3c5 ≠ 26, r3c6 ≠ 27, r4c6 ≠ 27, r5c5 ≠ 26, r5c6 ≠ 27, r6c5 ≠ 26, r6c6 ≠ 27
whip[1]: n21{r4c4 .} ==> r5c6 ≠ 22
z-chain[2]: n22{r5c5 r2c2} - n20{r2c2 .} ==> r1c3 ≠ 21
z-chain[2]: n21{r1c1 r2c2} - n23{r2c2 .} ==> r1c3 ≠ 22
z-chain[2]: n22{r1c1 r2c2} - n24{r2c2 .} ==> r1c3 ≠ 23
whip[1]: r1c3{n20 .} ==> r1c1 ≠ 19, r4c2 ≠ 20, r4c3 ≠ 20, r4c4 ≠ 20, r2c1 ≠ 19, r3c1 ≠ 19, r3c3 ≠ 19
whip[1]: n20{r3c3 .} ==> r3c5 ≠ 21, r3c6 ≠ 22, r4c6 ≠ 22
z-chain[2]: n22{r4c4 r3c5} - n24{r3c5 .} ==> r3c6 ≠ 23
z-chain[2]: n22{r4c3 r4c4} - n24{r4c4 .} ==> r3c5 ≠ 23
z-chain[2]: n21{r3c3 r2c2} - n19{r2c2 .} ==> r1c3 ≠ 20
whip[1]: r1c3{n19 .} ==> r1c1 ≠ 18, r2c1 ≠ 18
whip[1]: r1c1{n28 .} ==> r6c1 ≠ 24, r6c2 ≠ 24, r6c3 ≠ 24, r6c4 ≠ 24, r6c5 ≠ 24
hidden-pairs: {n18 n19}{r1c3 r2c2} ==> r2c2 ≠ 33, r2c2 ≠ 29, r2c2 ≠ 28, r2c2 ≠ 27, r2c2 ≠ 24, r2c2 ≠ 23, r2c2 ≠ 22, r2c2 ≠ 21, r2c2 ≠ 20
S+W1 tte

[watsies]

Hi. I'm new to this forum but I came across this thread some weeks ago and the information here has inspired and helped me to develop an Hidato app for Android devices called Hidoku Challenge. Please check it out.

https://play.google.com/store/apps/deta ... u&hl=en_us

It's totally free to install and use and is ad-free. Please enjoy it.

[watsies]

Correction! Google Play Hidoku Challenge link: https://play.google.com/store/apps/details?id=com.ajay.hidoku

[denis_berthier]

HI watsies,
Welcome to this forum.
I don't have android and can't try your app.
Why don't you say more about it here, so that we don't think you registered only for advertising it?

[watsies]

You are correct! The purpose of my entry is to advertise it to yourselves but not for any financial gain, it's totally free and doesn't contain ads, but for Hidato lovers like yourselves to have another puzzle generator at your fingertips. I apologise if this is not in keeping with the thread.

My wife loves Hidato and buys the books so I thought I'd try to understand the puzzle itself so that I could attempt an Android app for her to use (we only have Samsung and Sony devices!). This forum, and particularly this thread helped me understand the process of puzzle creation and solving techniques needed to assist creation. I was more successful than I'd hoped and the app was good enough to upload to Google Play.

As described on Google Play I've generated 500 puzzles from 5x5 to 18x18 both square and rectangular with a variety of hole patterns to provide variation. None are too difficult but are challenging enough to make Hidato enjoyable for novices and, hopefully, experienced players too. Unlike other Hidato/Hidoku apps this doesn't have a number pad - I decided that (smart) number selection rather than entry made it easier to use.

It it proves popular I will generate further puzzles and maybe 'up' the challenge. Such is my enthusiasm for this genre I'm now working on Suguru Challenge! My wife loves this too and I have found the same techniques can be ported across to generating challenging Suguru puzzles - but that's another thread!

[jco]

Bonjour Denis,

Est-ce qu'on est permis de parler francais ici?
Je viens de creer un autre hidoku.

Andrew

https://andrewspuzzles.blogspot.com/202 ... -by-5.html

Nice little puzzle!

Code: Select all

,--------------------,
| __  __  __  19  __ | 5
| __  25  __  __  __ | 4
| __  15  __  __  __ | 3
| __  __  01  __  03 | 2
| __  __  __  __  __ | 1
'--------------------'
  a   b   c   d   e   International_DBA

Part 1: (16)c4 Reasoning:

Code: Select all

. (16)a2 or (16)a3 imply that we cannot reach 19.
. (16)a4 forces (17)b5 so no number for a5.
. (16)b2 forces (17)c3 and,
        . if (18)c4, then the route from 14 to 3
          has to pass through a2,a1,b1,c1,d1,e1,d2,
          not reaching 04. Notice that a5,b5,c5 is
          taken for numbers 24,23,22.
        . if (18)d4, then (20)e5, (21)e4 and the
          path to 25 has to pass through c4,d3 so
          we must have (2)d1,(4)e1,(5)d2, (6)c1,
          (7)b1, etc and the connection to 15 is lost.

Part 2: (17)d4 Reasoning:

Code: Select all

. (17)b5 forces (18)c5, (24)a5, (23)a3, etc,
  and the connection between 25 and 19 is lost.
. (17)c5 forces (18)d4, (20)e5, (21)e4,
  (24)b5, (23)a5; connection to 21 is lost.
. (17)c3 forces (18)d4, (20)e5,(21)a4;
  and the connection between 21 and 25 is lost.
. (17)d3 forces (18)d4 or (18)e4:
        . in the first case we need (20)e5
          and (24)c5 and the connection between
          20 and 25 is lost;
        . in the second case, i.e., (18)e4,
          forces (20)e5, (21)d3, reaching a
          problem in cells e1, e3 (only one access)

Part 3: 3.(18)e5 4.(20)c5 5.(21)b5 6.(22)a5 7.(23)a4 8.(24)a3

Code: Select all

,--------------------,
|*22 *21 *20  19 *18 | 5
|*23  25 *16 *17  __ | 4
|*24  15  __  __  __ | 3
| __  __  01  __  03 | 2
| __  __  __  __  __ | 1
'--------------------'
  a   b   c   d   e

Part 4: 9.(2)d1 Reasoning:

Code: Select all

  . (2)d3 creates a problem at e3,e4,
    that can be accesses in only one way
  . (2)d2 makes e4 to be reached in only
    one way.

Part 4: only singles!

Code: Select all

,--------------------,
|*22 *21 *20  19 *18 |
|*23  25 *16 *17 *07 |
|*24  15 *09 *08 *06 |
|*14 *10  01 *05  03 |
|*13 *12 *11 *02 *04 |
'--------------------'

EDIT: corrected typo.

[denis_berthier]

.
As I haven't been solving Hidatos for some time, I tried this puzzle. It's quite hard but it can be solved without any T&E technique.

The HidatoRules command is:

Code: Select all

 (solve Hidato geometric 5 25
. . . 19 .
. 25 . . .
. 15 . . .
. . 1 . 3
. . . . .
)

and the solution is in W8:

Hidden Text: Show

Code: Select all

*****  Hidato-Rules geometric-model   *****
Resolution state after Singles:
240 candidates, 3110 csp-links and 7188 links. Density = 25.06%
whip[1]: r5c1{n10 .} ==> r5c5≠10, r1c1≠10, r1c2≠10, r1c3≠10, r1c5≠10, r2c5≠10, r3c5≠10
whip[1]: n14{r4c2 .} ==> r5c4≠13
whip[1]: n17{r3c4 .} ==> r4c1≠16, r3c1≠16
whip[1]: n21{r3c5 .} ==> r4c1≠22, r3c1≠22

Resolution state after Singles and whips[1]:
228 candidates.

whip[2]: r5c1{n11 n7} - r5c5{n8 .} ==> r3c5≠11, r1c1≠11, r1c2≠11, r1c3≠11, r1c5≠11, r2c5≠11
whip[2]: n11{r5c5 r2c4} - n13{r1c1 .} ==> r1c5≠12
whip[2]: r5c2{n9 n13} - r5c1{n13 .} ==> r1c5≠9, r1c1≠9, r1c2≠9, r1c3≠9
whip[2]: n11{r5c5 r3c1} - n9{r5c5 .} ==> r2c1≠10
whip[3]: r5c1{n11 n7} - r4c1{n7 n23} - r1c1{n22 .} ==> r5c5≠11
whip[2]: r5c5{n9 n12} - r5c1{n9 .} ==> r1c1≠7, r1c2≠6, r1c2≠7, r1c3≠6, r1c3≠7, r1c5≠6, r1c5≠7, r2c1≠7, r3c1≠7
whip[1]: n7{r5c5 .} ==> r1c1≠8, r2c1≠8
whip[3]: n23{r4c4 r2c4} - n21{r2c4 r2c5} - n20{r1c3 .} ==> r1c5≠22
whip[4]: r5c1{n9 n13} - n11{r5c1 r3c3} - r5c2{n11 n6} - n7{r2c3 .} ==> r2c5≠9
whip[5]: r5c5{n9 n12} - n13{r1c1 r4c4} - n11{r4c4 r5c4} - n4{r5c4 r3c4} - n2{r3c4 .} ==> r5c1≠7
whip[4]: r5c1{n13 n8} - r5c5{n9 n4} - r4c1{n7 n23} - r1c1{n22 .} ==> r2c5≠12
whip[4]: r5c1{n13 n8} - r5c5{n9 n4} - r4c1{n7 n23} - r1c1{n22 .} ==> r3c5≠12
whip[5]: r5c5{n9 n12} - n13{r1c1 r4c4} - n11{r4c4 r5c4} - n4{r5c4 r3c4} - n2{r3c4 .} ==> r4c1≠7
whip[3]: r5c1{n13 n8} - r4c1{n8 n23} - r1c1{n22 .} ==> r5c5≠12
whip[3]: n5{r5c5 r5c3} - n7{r5c3 r4c2} - r5c5{n9 .} ==> r5c2≠6
whip[4]: r5c1{n12 n13} - r5c2{n13 n7} - n8{r1c2 r4c2} - n12{r4c2 .} ==> r2c4≠10
whip[5]: r5c1{n13 n8} - n10{r2c3 r5c3} - n12{r5c3 r4c4} - r4c1{n10 n23} - r1c1{n22 .} ==> r5c4≠11
whip[5]: r5c1{n12 n13} - n11{r2c1 r3c3} - r5c2{n12 n7} - n9{r2c1 r3c4} - n8{r1c2 .} ==> r2c3≠10
whip[6]: r5c5{n8 n9} - r5c1{n8 n13} - n12{r1c1 r5c2} - n11{r2c1 r5c3} - n7{r5c3 r3c3} - n5{r3c3 .} ==> r4c2≠6
whip[6]: r5c5{n8 n9} - n8{r1c2 r4c4} - n10{r3c1 r5c4} - n2{r5c4 r3c4} - n7{r3c4 r3c5} - n4{r3c5 .} ==> r2c5≠6
whip[6]: n24{r3c1 r2c1} - n22{r2c1 r4c2} - n21{r3c5 r3c3} - n16{r3c3 r2c3} - n14{r2c3 r4c1} - r1c1{n12 .} ==> r3c1≠23
whip[3]: n21{r3c5 r1c2} - n23{r4c4 r1c1} - n24{r1c3 .} ==> r2c1≠22
whip[6]: r5c5{n8 n9} - r5c1{n8 n13} - r3c1{n14 n24} - r1c1{n23 n22} - r1c5{n20 n18} - n17{r1c2 .} ==> r2c4≠6
whip[6]: r5c5{n8 n9} - r5c1{n8 n13} - r3c1{n14 n24} - r1c1{n23 n22} - r1c5{n20 n18} - r2c5{n18 .} ==> r2c3≠6
whip[7]: n14{r4c2 r2c1} - n12{r2c1 r1c2} - r5c1{n13 n8} - n11{r5c1 r2c3} - n10{r5c4 r3c3} - r4c1{n10 n23} - n21{r1c2 .} ==> r1c1≠13
whip[4]: n22{r4c2 r3c3} - r1c1{n23 n12} - n10{r3c4 r3c1} - n24{r3c1 .} ==> r4c2≠23
whip[4]: n22{r4c4 r4c2} - r1c1{n24 n12} - r5c1{n13 n8} - n9{r2c1 .} ==> r4c1≠23
whip[2]: n21{r3c5 r3c3} - n23{r3c3 .} ==> r4c2≠22
whip[4]: r5c1{n13 n8} - r4c1{n8 n14} - n13{r1c2 r4c2} - n9{r4c2 .} ==> r2c4≠11
whip[4]: r5c1{n13 n8} - n11{r5c1 r2c3} - r4c1{n12 n9} - n10{r3c3 .} ==> r1c3≠12
whip[4]: r1c1{n24 n12} - r5c1{n13 n8} - r3c5{n5 n4} - r5c5{n5 .} ==> r1c5≠21
whip[4]: r1c1{n24 n12} - n11{r2c3 r2c1} - n13{r2c4 r1c2} - n14{r3c1 .} ==> r2c3≠23
whip[4]: r1c1{n24 n12} - r5c1{n13 n8} - r1c5{n8 n18} - r1c3{n17 .} ==> r4c4≠22
whip[5]: r1c1{n24 n12} - n11{r2c3 r2c1} - n24{r2c1 r2c3} - n13{r2c3 r1c2} - n14{r3c1 .} ==> r3c3≠23
whip[5]: r1c1{n24 n12} - n11{r2c3 r2c1} - n13{r2c4 r1c2} - n14{r3c1 r2c3} - n24{r2c3 .} ==> r1c3≠23
whip[5]: r5c1{n13 n8} - n10{r3c4 r3c3} - r4c1{n11 n14} - n12{r1c1 r2c3} - n13{r2c1 .} ==> r3c4≠11
whip[5]: r5c1{n13 n8} - r4c1{n8 n14} - r3c1{n14 n24} - r3c5{n21 n4} - r5c5{n5 .} ==> r4c4≠11
whip[6]: r1c1{n24 n12} - r5c1{n13 n8} - r1c5{n8 n18} - r1c3{n18 n24} - n23{r1c1 r2c4} - n17{r2c4 .} ==> r3c5≠21
whip[4]: r1c1{n24 n12} - r5c1{n13 n8} - r5c5{n9 n4} - r3c5{n5 .} ==> r2c4≠22
whip[4]: r1c1{n24 n12} - r5c1{n13 n8} - r5c5{n9 n4} - r3c5{n5 .} ==> r2c5≠22
whip[4]: r1c1{n24 n12} - r5c1{n13 n8} - r5c5{n9 n4} - r3c5{n5 .} ==> r3c4≠22
whip[4]: r5c5{n9 n4} - r3c5{n5 n22} - r1c1{n23 n12} - r5c1{n13 .} ==> r4c1≠8
whip[4]: r5c5{n9 n4} - r3c5{n5 n22} - r1c1{n23 n12} - r5c1{n13 .} ==> r3c1≠8
whip[4]: r5c5{n9 n4} - r3c5{n5 n22} - r1c1{n23 n12} - r4c1{n13 .} ==> r1c2≠8
whip[1]: n8{r5c5 .} ==> r2c1≠9
whip[4]: r5c1{n13 n8} - r5c5{n9 n4} - r3c5{n5 n22} - r1c1{n23 .} ==> r2c3≠11
whip[4]: r5c1{n13 n8} - r5c5{n9 n4} - r3c5{n5 n22} - r1c1{n23 .} ==> r1c2≠12
whip[3]: n14{r2c1 r3c1} - n12{r5c4 r1c1} - n11{r3c1 .} ==> r2c1≠13
whip[5]: r4c1{n14 n9} - r3c1{n9 n24} - n23{r1c1 r2c1} - r1c5{n20 n18} - n17{r1c2 .} ==> r2c4≠12
whip[2]: n14{r4c2 r2c3} - n12{r5c4 .} ==> r1c3≠13
whip[3]: n14{r2c3 r3c3} - n12{r3c3 r3c4} - n11{r2c1 .} ==> r2c3≠13
whip[5]: r4c1{n14 n9} - r5c1{n9 n8} - r5c5{n9 n4} - r3c5{n5 n22} - r1c1{n23 .} ==> r5c4≠12
whip[5]: r4c1{n14 n9} - r5c1{n9 n8} - r5c5{n9 n4} - r3c5{n5 n22} - r1c1{n23 .} ==> r4c4≠12
whip[5]: r4c1{n14 n9} - r5c1{n9 n8} - r5c5{n9 n4} - r3c5{n5 n22} - r1c1{n23 .} ==> r3c4≠12
whip[5]: r5c5{n9 n4} - r3c5{n5 n22} - r1c1{n23 n12} - r5c1{n13 n8} - r5c2{n8 .} ==> r4c2≠7
whip[6]: r1c1{n24 n12} - r4c1{n14 n9} - r5c1{n9 n8} - r4c2{n8 n16} - r1c5{n18 n20} - r1c3{n21 .} ==> r3c4≠23
whip[6]: r1c1{n24 n12} - r4c1{n14 n9} - r5c1{n9 n8} - r4c2{n8 n16} - n17{r1c2 r3c3} - n24{r3c3 .} ==> r4c4≠23
whip[5]: n23{r2c1 r2c4} - r1c1{n22 n12} - r5c1{n13 n8} - r3c5{n5 n4} - r5c5{n5 .} ==> r3c3≠22
whip[6]: n23{r2c1 r2c4} - r1c1{n22 n12} - r4c1{n13 n9} - r5c1{n9 n8} - r4c2{n8 n16} - n17{r1c2 .} ==> r3c3≠24
whip[7]: r5c1{n9 n13} - r4c1{n13 n14} - r3c1{n14 n24} - n23{r1c1 r2c1} - r1c5{n20 n18} - r4c2{n16 n12} - r5c2{n12 .} ==> r3c5≠9
whip[4]: r5c5{n9 n4} - r3c5{n5 n22} - r1c1{n23 n12} - r5c1{n13 .} ==> r2c3≠7
whip[7]: r5c1{n9 n13} - r4c1{n13 n14} - r3c1{n14 n24} - n23{r1c1 r2c1} - r1c5{n20 n18} - r4c2{n16 n12} - r5c2{n12 .} ==> r5c5≠9
whip[4]: r5c5{n7 n8} - r3c5{n7 n22} - r1c1{n23 n12} - r4c1{n13 .} ==> r2c3≠5
whip[6]: r5c5{n7 n8} - n7{r2c4 r4c4} - n9{r3c1 r5c4} - n2{r5c4 r3c4} - n4{r3c4 r3c5} - n6{r3c5 .} ==> r2c5≠5
whip[8]: r5c1{n13 n8} - n11{r5c1 r2c1} - n13{r2c4 r1c2} - n14{r3c1 r2c3} - r4c1{n14 n9} - r4c2{n9 n16} - n18{r2c5 r2c4} - n23{r2c4 .} ==> r1c1≠12
whip[1]: r1c1{n24 .} ==> r2c4≠23, r2c5≠21, r3c5≠22
whip[2]: r5c5{n8 n4} - r3c5{n5 .} ==> r5c2≠7, r5c1≠8
whip[1]: r5c1{n13 .} ==> r2c1≠11
whip[3]: r1c1{n24 n22} - n21{r1c3 r1c2} - n23{r1c2 .} ==> r2c3≠24
whip[3]: r1c1{n24 n22} - n21{r1c3 r1c2} - n23{r1c2 .} ==> r1c3≠24
whip[3]: n17{r3c4 r1c2} - n23{r1c2 r1c1} - n24{r3c1 .} ==> r2c1≠16
whip[3]: n11{r5c3 r3c3} - n16{r3c3 r4c2} - n17{r1c2 .} ==> r2c3≠12
whip[3]: n12{r5c3 r4c2} - n14{r4c2 r2c3} - n16{r2c3 .} ==> r3c3≠13
whip[3]: n12{r5c3 r2c1} - n23{r2c1 r1c1} - n24{r3c1 .} ==> r1c2≠13
whip[2]: n11{r5c3 r3c1} - n13{r4c4 .} ==> r2c1≠12
whip[3]: n22{r1c3 r2c3} - n16{r2c3 r4c2} - n17{r1c2 .} ==> r3c3≠21
whip[4]: n12{r5c3 r3c3} - n14{r3c3 r2c3} - n16{r2c3 r4c2} - n17{r1c2 .} ==> r2c4≠13
whip[4]: n13{r5c3 r3c4} - n12{r3c1 r3c3} - n11{r3c1 r4c2} - n16{r4c2 .} ==> r2c3≠14
whip[2]: n12{r5c3 r3c3} - n14{r3c3 .} ==> r3c4≠13
whip[3]: n11{r5c3 r4c2} - n13{r4c2 r4c4} - n14{r2c1 .} ==> r3c3≠12
whip[4]: n16{r4c2 r2c3} - n18{r2c3 r1c3} - n22{r1c3 r1c1} - n21{r1c3 .} ==> r1c2≠17
whip[4]: r5c1{n12 n13} - n11{r5c1 r3c3} - r5c2{n12 n8} - n9{r2c3 .} ==> r3c4≠10
whip[3]: n10{r5c4 r3c3} - n11{r3c1 r4c2} - n16{r4c2 .} ==> r2c3≠9
whip[2]: n7{r5c5 r2c4} - n9{r5c4 .} ==> r1c3≠8
whip[6]: n12{r5c3 r4c2} - n10{r4c2 r4c4} - r5c1{n11 n13} - r5c2{n13 n8} - n7{r2c4 r5c3} - n9{r2c4 .} ==> r3c3≠11
whip[7]: n9{r5c4 r2c4} - n7{r5c3 r2c5} - n10{r3c1 r3c3} - n11{r3c1 r4c2} - n16{r4c2 r2c3} - n18{r2c3 r1c3} - n17{r3c3 .} ==> r1c5≠8
whip[2]: r1c5{n20 n18} - r1c3{n17 .} ==> r3c4≠21
whip[2]: r1c5{n20 n18} - n17{r1c3 .} ==> r2c4≠20
whip[2]: r1c5{n18 n20} - n21{r1c2 .} ==> r2c4≠18
whip[2]: n16{r4c2 r2c3} - n18{r2c3 .} ==> r1c3≠17
whip[3]: n18{r2c5 r1c3} - r1c5{n18 n20} - n22{r1c1 .} ==> r2c3≠17
whip[3]: r1c5{n20 n18} - n17{r3c4 r2c4} - n21{r2c4 .} ==> r2c5≠20
whip[3]: r1c5{n18 n20} - n21{r1c2 r2c4} - n17{r2c4 .} ==> r1c3≠18
whip[4]: n10{r5c4 r3c3} - n17{r3c3 r3c4} - r1c5{n18 n20} - n21{r1c2 .} ==> r2c4≠9
whip[4]: r5c5{n7 n8} - r2c5{n8 n18} - r1c5{n18 n20} - n21{r1c2 .} ==> r2c4≠5
whip[5]: r2c5{n8 n18} - r1c5{n18 n20} - r1c1{n22 n24} - r2c1{n24 n14} - r5c1{n12 .} ==> r5c5≠8
whip[2]: r5c5{n6 n7} - r3c5{n6 .} ==> r3c3≠5, r5c3≠5
whip[4]: r5c5{n6 n7} - n6{r3c3 r4c4} - n2{r4c4 r5c4} - n8{r5c4 .} ==> r3c4≠5
whip[5]: r5c5{n6 n7} - n6{r3c3 r4c4} - n8{r4c4 r5c4} - n2{r5c4 r3c4} - n4{r3c4 .} ==> r3c5≠5
whip[2]: r3c5{n8 n4} - r5c5{n5 .} ==> r3c3≠7, r3c1≠9, r4c1≠9, r5c1≠9, r5c3≠7, r4c2≠8, r5c2≠8
whip[2]: r5c1{n13 n10} - r4c1{n10 .} ==> r4c4≠13
whip[4]: r3c5{n8 n4} - n5{r5c4 r4c4} - n6{r4c4 r5c4} - n8{r2c3 .} ==> r5c5≠7
whip[3]: n7{r5c4 r4c4} - n5{r4c4 r5c5} - n4{r3c4 .} ==> r5c4≠8
whip[3]: n7{r5c4 r4c4} - n5{r4c4 r5c5} - n4{r3c4 .} ==> r5c4≠6
whip[4]: r5c5{n5 n6} - r3c5{n7 n8} - n9{r3c3 r4c4} - n5{r4c4 .} ==> r3c4≠4
whip[4]: n11{r5c2 r5c3} - n9{r5c3 r4c4} - n5{r4c4 r5c5} - n4{r3c5 .} ==> r5c4≠10
whip[5]: r5c1{n13 n10} - n8{r2c3 r3c3} - n9{r5c2 r4c2} - n11{r4c2 r5c2} - n13{r5c2 .} ==> r5c3≠12
whip[5]: r2c5{n8 n18} - n16{r4c2 r3c3} - n9{r3c3 r3c4} - n7{r3c4 r2c4} - n17{r2c4 .} ==> r2c3≠8
whip[5]: r2c5{n8 n18} - r1c5{n18 n20} - r1c1{n22 n24} - r2c1{n24 n14} - r5c1{n12 .} ==> r5c4≠9
whip[5]: r2c5{n8 n18} - r1c5{n18 n20} - r1c1{n22 n24} - r2c1{n24 n14} - n13{r4c1 .} ==> r3c1≠10
whip[6]: r5c5{n6 n4} - r3c5{n4 n8} - r5c4{n7 n2} - n5{r5c4 r4c4} - n9{r4c4 r3c4} - n10{r4c1 .} ==> r3c3≠6
whip[6]: r5c1{n13 n10} - r2c5{n7 n18} - r1c5{n18 n20} - r1c1{n22 n24} - r2c1{n24 n14} - n13{r4c1 .} ==> r3c1≠12
whip[6]: r5c1{n12 n13} - r5c2{n13 n9} - r2c5{n7 n18} - r1c5{n18 n20} - r1c1{n22 n24} - r2c1{n24 .} ==> r3c1≠11
whip[6]: r5c5{n6 n4} - r3c5{n4 n8} - n7{r5c4 r4c4} - n9{r4c4 r3c4} - n2{r3c4 r5c4} - n5{r5c4 .} ==> r5c3≠6
whip[7]: r2c5{n8 n18} - r1c5{n18 n20} - n21{r1c2 r2c4} - n17{r2c4 r3c4} - n2{r3c4 r4c4} - n6{r4c4 r5c5} - n5{r5c5 .} ==> r5c4≠7
whip[3]: n7{r3c5 r4c4} - n5{r4c4 r5c4} - n4{r3c5 .} ==> r5c5≠6
whip[1]: r5c5{n5 .} ==> r3c5≠4
whip[2]: r5c5{n4 n5} - n6{r3c4 .} ==> r4c4≠4
whip[3]: r3c5{n8 n6} - n5{r5c4 r4c4} - n7{r4c4 .} ==> r5c3≠8
whip[1]: n8{r4c4 .} ==> r5c2≠9
whip[2]: r5c3{n11 n13} - r4c1{n12 .} ==> r3c3≠10
whip[3]: r5c3{n11 n13} - n14{r2c1 r4c2} - n9{r4c2 .} ==> r5c1≠10
whip[3]: r5c3{n11 n13} - n14{r2c1 r4c2} - n9{r4c2 .} ==> r4c1≠10
whip[2]: r5c1{n13 n11} - r4c1{n11 .} ==> r5c3≠13
whip[3]: n10{r5c3 r4c4} - n6{r4c4 r3c5} - n5{r5c4 .} ==> r3c4≠9
whip[1]: n9{r5c3 .} ==> r2c5≠8
whip[3]: n9{r5c3 r4c4} - n6{r4c4 r3c4} - n5{r5c4 .} ==> r3c5≠8
whip[2]: r3c5{n7 n6} - n5{r5c4 .} ==> r4c4≠7
whip[3]: r2c5{n7 n18} - r1c5{n18 n20} - n21{r1c2 .} ==> r2c4≠7
whip[3]: r2c5{n18 n7} - n9{r4c2 r4c4} - n5{r4c4 .} ==> r3c3≠17
whip[1]: n17{r3c4 .} ==> r4c2≠16
whip[3]: n17{r2c4 r3c4} - r1c5{n18 n20} - n21{r1c2 .} ==> r2c4≠8
whip[3]: n5{r5c5 r4c4} - n8{r4c4 r3c3} - n7{r2c5 .} ==> r3c4≠6
whip[2]: n6{r4c4 r3c5} - n5{r5c4 .} ==> r4c4≠2, r4c4≠8, r4c4≠9, r4c4≠10
whip[1]: n8{r3c4 .} ==> r5c3≠9
whip[1]: r5c3{n11 .} ==> r4c1≠11, r5c1≠11
whip[1]: r5c1{n13 .} ==> r2c1≠14, r3c1≠13
biv-chain[2]: n9{r3c3 r4c2} - n8{r3c4 r3c3} ==> r3c3≠14, r3c3≠16
hidden-single: r2c3=16
whip[1]: n20{r1c5 .} ==> r1c3≠21
whip[1]: n21{r2c4 .} ==> r1c2≠22
whip[1]: n22{r1c3 .} ==> r1c1≠23
biv-chain[2]: r2c1{n24 n23} - n21{r2c4 r1c2} ==> r1c2≠24
biv-chain[2]: r2c1{n24 n23} - n22{r1c3 r1c1} ==> r1c1≠24
stte

.