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 Difficult 9x9 Tuesday April 23rd 2019 
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Posted on: Wed Apr 24, 2019 2:26 pm




Posts: 510
Location: Dublin, Ireland
Joined: Tue Mar 01, 2016 10:03 pm
Post Difficult 9x9 Tuesday April 23rd 2019
Yesterday's difficult 9x9 was not the usual type of pattern. I found it extremely difficult to,solve and have only just managed to complete it a few minutes ago. I note that it's only been solved 70 times, so it looks like I'm not the only one who has struggled with it..


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Posted on: Wed Apr 24, 2019 6:25 pm




Posts: 510
Location: Dublin, Ireland
Joined: Tue Mar 01, 2016 10:03 pm
Post Re: Difficult 9x9 Tuesday April 23rd 2019
paulv66 wrote:
Yesterday's difficult 9x9 was not the usual type of pattern. I found it extremely difficult to,solve and have only just managed to complete it a few minutes ago. I note that it's only been solved 70 times, so it looks like I'm not the only one who has struggled with it..


I had a look at the number of times the Tuesday difficult 9x9 was solved over the past month. The numbers are as follows:

26/03/19 235
02/04/19 217
09/04/19 169
16/04/19 259
23/04/19 73 (so far)

I know there's nearly six hours left within which yesterday's puzzle will earn points, but it seems likely that the final number will be a lot lower than average. I'd be curious to know what's the lowest number of solvers for the Tuesday 9x9 in recent years.


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Posted on: Wed Apr 24, 2019 6:45 pm




Posts: 206
Joined: Thu May 12, 2011 11:51 pm
Post Re: Difficult 9x9 Tuesday April 23rd 2019
I agree -- this format tends to be more difficult and this iteration was more difficult. I did not have time to wrestle with it so won't be one of the few solvers.


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Posted on: Wed Apr 24, 2019 8:12 pm




Posts: 395
Joined: Wed Apr 16, 2014 9:20 pm
Post Re: Difficult 9x9 Tuesday April 23rd 2019
The pattern of this particular 9 x 9 is extremely difficult.

it is know as the hardest 9 x 9 pattern to solve, at least I think that is what Patrick has stated.

What I was surprised at , is that we had this pattern about a month ago (sometime in late Feb or March) and I thought we would be done with it for the year.


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Posted on: Thu Apr 25, 2019 1:45 am




Posts: 268
Joined: Sun May 22, 2016 2:17 pm
Post Re: Difficult 9x9 Tuesday April 23rd 2019
That pattern was the most difficult puzzle in 121 Advanced Puzzles VII for sure. I only solved it a few weeks ago after months of trying.


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Posted on: Thu Apr 25, 2019 8:07 am




Posts: 36
Joined: Tue Mar 10, 2015 5:59 pm
Post Re: Difficult 9x9 Tuesday April 23rd 2019
I especially found it more difficult at the start of the puzzle.
After that, it was not really hard anymore, so the puzzle didn't take me much longer than other Tuesday 9x9s.
However, I always solve the hardest puzzles by guessing, so I don't know how hard it was to solve it analitically, although I only used one guess.
This guess was a really bad guess, too, I was still able to fill in the other option and change a few numbers as the guess turned out to be wrong, having already filled in almost the complete puzzle.


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Posted on: Wed May 01, 2019 10:00 am




Posts: 39
Joined: Sun Feb 03, 2013 3:25 am
Post Re: Difficult 9x9 Tuesday April 23rd 2019
Hallo, I would like to introduce my ”step by step“ solution of this hard nut, and compare to yours if… [rolleyes] (The order of steps is not necessarily chronologic.)

First (basic) eliminations/thoughts:
0 a) CD4 ≠ [8,9] (due to CD6 and “rule” of unique solution; it would already be eliminated after step 1) (later) though);
b) interaction between FG4 and FG6 – F4 ≠ 4 and G4 ≠ 1;
c) H4 ≠ 6;
d) the right 1512× cage has combinations [3,7,8,9] and [4,6,7,9];
e) rule of parity says that three rows or columns in a 9×9 calcudoku must get an odd result (3 × 45). So if the right 1512× cage is [3,7,8,9], G4 = [3,7]; if is [4,6,7,9], G4 = [4,6,8];
f) the central 324× cage can by composed of digits 1, 2, 3, 4, 6 and 9.

Image

1) (Im)possible combinations for the central 324× cage: [1,1,4,9,9], [1,1,6,6,9], [1,2,2,9,9], [1,2,3,6,9], [1,3,3,4,9], [1,3,3,6,6], [2,2,3,3,9], [2,3,3,3,6] and [3,3,3,3,4].
Of these, only two are valid: [1,2,3,6,9] and [1,3,3,4,9] (number 4 can only be in E5!). It means that the column E contains 1 in E4 or E6, the row 5 contains 9 in D5 or F5. Thus 9 in the right 1512× cage must be placed in the row 4 – I4 = 9.

Image

2) Needed a long chain on 7 in H6, but it was very useful.
If H6 = 7 → H8 = 1, B7 = 7 (due to no other place for the third 7 in lower three rows), B6 = 3, G6 = 1, E6 = 2, A6 = 5, I6 = 6, H5 = 4, DEF5 = [3,6,9], AB5 = [2,8], A4 = 6; H5678 = [1,4,6,7], thus H34 = [2,3].
Now the sum of known numbers in the columns G, H and I is 117, so G2 + H2 + G4 = 18. G4 ≠ 6; if G4 = 8, GH2 is blocked; if G4 = 4, GH2 = [6,8].
This with three 7's in the columns A, B and C means that BC2 = [2,9]. The “rule” of unique solution is again on the scene: BC8 ≠ [2,9] = [5,6].
Now factorial counting the three left columns: 9!^3 ÷ (cages by rows: 2160 × 18 × 7 × 480 × 21 × 1512 × 3 × 30) = 128.
So the cells B3, B4, C4 and C6 must get product of 128 = 2^7; C6 = 8, C4 = 2, B34 = product of 8, which is impossible → H6 ≠ 7
It gives sure 7 for the 21+ cage. Also the 10+ and the upper 11+ cage ≠ 7.

Image

3) If B6 = 2 → H6 = 6, FG6 = [1,4], A6 = 5, E6 = 3, I6 = 7; if HI5 = [4.6], the 324× cage is blocked; if [3,8], DEF5 = [2,6,9], AB5 = [4,7], A4 = 5. A4 = A6 – contradiction, therefore B67 ≠ [2,8] = [4,6]. B34 = 1–3 and a little bit eliminations…

Image

4) If H6 = 6 → G8 = 7, G6 = 3; so G4 is even and the right 1512× cage must be [4,6,7,9]; H5 = 4, H8 = 1, H34 = again [2,3]. And again the sum of the columns G, H and I: this time 119, so G2 + H2 + G4 = 16.
All possibilities of numbers 5, 8, and 9 in H2 lead to contradiction, thus H6 ≠ 6 = 5.

Image

5) Another long chain:
If the right 1512× cage = [3,7,8,9] → in cooperation with B5 = [3,7,8], DEF5 must be [2,6,9], A5 = 4; E46 = [1,3], therefore HI5 = [3,8], B5 = 7, I6 = 7, A6 = [2,4,6]; A4 + A6 = 10 and A5 = 4, thus A6 = 2, A4 = 8; G6 = 1, G8 = 7, G4 = 3 (rule of parity), F4 = 2, E4 = 1. But now exists no number for B4, so the right 1512× cage = [4,6,7,9]. Which created naked triple of 4, 6 and 7 in I567

Image

6) a) G4 = [4,6,8];
b) the 21+ cage contains 8; therefore remaining digits are 1, 2, 3, 4 and 5 and A4 = 2–5;
c) E8 ≠ [2,5] = [4,6];
d) I789 = min. 15 → A) I9 ≠ [1,2,5] = [3,8]; B) if I7 = 4 → A7 = 7, G9 or H9 = 7 – no combination for the sum of 21 here, thus I7 = [6,7];
e) H5 = [6,7] → H34 = 1–4

Image

7) If E5 = 4 → DF5 = [3,9], HI5 = [6,7], AB5 = [2,8], A4 + A6 = 11, which makes combination [4,7] here; E8 = 6, A8 = 4. A4 = A8 – contradiction, therefore the central 324× cage = [1,2,3,6,9].

Image

8) If FG6 = [1,4] → B6 = 6, HI5 = [4,6], but it forces numbers 1 and 6 to one cell (E4). FG6 = [2,3].

Image

9) Due to the 324× cage, the 21+ cage ≠ 3 (otherwise three 3's in two rows). It is applicable the rule of parity for the three central rows: sum of known cells/cages is odd, so BH4 must be even… [1,3] or [2,4]. If BH4 = [2,4] → A4 = 5, the two subtraction cages are blocked. Thus BH4 = [1,3], B3 = 2, H3 = 4.

Image

10) At the end the rule of parity helps again: A4 = even ≠ 5the 21+ cage = [2,4,7,8], A78 ≠ 4. Etc… [razz]

Image


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Posted on: Thu May 09, 2019 1:14 am




Posts: 59
Joined: Sun Jan 31, 2016 7:52 am
Post Re: Difficult 9x9 Tuesday April 23rd 2019
This is an old topic but I have been busy, if anybody is still interested in this puzzle I have listed my steps to solve the puzzle.
It is an interesting puzzle, the 32+ cage in the lower right corner is more help than it might look to begin with.
If anybody would like a more detailed description of the steps taken to solve the puzzle I am happy to provide more information.

d7=5, d8=3
cage g8(7/) = 1,7
>> f8=8
cage c6(72x) = 8,9

cage e4(324x) : row 5 in cage must have 9
>> i4=9

i9 ≠ 7 (row 6 has no 7)
i9 ≠ 1 (row 9 has no 4)
i9 ≠ 2 (cage a7 has no possible solution)
g9 ≠ 3 (row 8 has no 4)

a8 ≠ 2 (row 8 has no 9)

a9 ≠ 9 (col b has no 8)
b9 ≠ 9 (col b has no 8)
c9 ≠ 9 (row 2 has no 8)
>> h9=9

a8 ≠ 6 (row 9 has no 7)
>> a8=9
>> cage b8 = 5,6

cage e8(120x) must have 5 in row 9
>> i9 ≠ 5

i9 ≠ 3 (cage h6(13+) has no solution )
i9 ≠ 6 (row 2 has no 8)
>> i9=8

g9 ≠ 7 (cage c6 (72x) has no solution)

From here the puzzle can be completed easily with basic level steps.


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