https://new.reddit.com/r/calcudoku/comm ... calcudoku/

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https://new.reddit.com/r/calcudoku/comm ... is_kenken/

(I crossposted it from r/numberpuzzles, and ran the puzzle through my solver, it is clearly an easy puzzle)

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https://new.reddit.com/r/calcudoku/comm ... ned_10x10/

should be fairly easy

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There are two main steps: (1) get the puzzle into an image file, (2) upload the image file

to "www.imgur.com" and link to it from your forum post:

For users of Windows:

1) make sure the puzzle is visible on the screen

2) press the "Print Screen" button (usually near the very top right of your keyboard)

3) run paintbrush: Start -> Run, type 'pbrush' + Enter

4) press Ctrl+V

5) if not already selected, select the "Rectangle select" tool (2nd icon at the top right of the toolbar)

6) drag out a rectangle around the puzzle

7) press Ctrl+C

8) press Ctrl+N (to the question "Save changes?" answer No)

9) press Ctrl+V

10) press Ctrl+S and type a filename. For "Save as type" select PNG

(note that for Windows there are lots of programs available that make this process simpler,

recommendations welcome)

(Mac users can do this in 1 step:

simply press Command+Shift+4 to take a screenshot of an area of the screen)

(Linux users simply press Alt+Print Screen to save window contents to a file)

In a browser window, start writing your forum post that is to include the puzzle image.

Now go to http://www.imgur.com, click "New Post", then "Choose Photo/Video"

and select the PNG file you just saved.

1) it should upload automatically

2) on the next page, hover over the top right of the image, and click on the three dots (...), select "Get share links",

then click the "Copy link" button next to the "BBCode (Forums)" entry

3) go to your forum post, place the cursor where you want the image, and press Ctrl+V

That should do it

Patrick

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This is the puzzle:

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6

-2,+,a1a2b2

12,*,b1c1

0,+,d1e1

4,*,f1f2f3

12,*,c2c3d3

8,*,d2e2e3

7,-,a3b3a4

0,+,b4c4

-1,+,d4e4

12,*,f4f5

-2,/,a5b5

1,+,c5d5c6

12,*,e5e6

8,*,a6b6

-1,d6

1,f6

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these analyses are actually very useful for improving my solver

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Here is how I solved it:

I don't know where to draw the line as to where a solution is considered to be T&E,

but here is a logical solution:

C1~1 (examine column C)

D1,D2~5

If we look at the cages in columns DEF all but the two 2: cages have a fixed parity.

Taking parity into consideration, one of the cages E56, F56 is {2,4} and the other {1,2} or {3,6}.

Now examine the possible values for the cage EF6. They must be {1,2}, {2,4}, {3,6}.

These interact strongly with the 60* cage at B5.

If EF6 is {1,2} then EF5={2,4}, D6=6, B5=1, D56={1,5}, D45={1,5} which is impossible.

If EF6 is {3,6} then D6=2, B5=3, EF5={2,4}, D5=5, D4=3, C45={1,6}, C23={2,4}, C6=5, C1=3.

This is also impossible because B1 is the only 5 remaining in Col B and B1,C1 must differ by 1.

This establishes that EF6={2,4}. Either D6=6 && B5=4 or D6=3 && B5=2.

The next step was to check the first possibility D6=6 && B5=4.

Note that since A6 is now odd and A3+A4+A5=10 that A1 and A2 have the same parity.

Thay obviously can't be {1,3} as that would require B2=8.

Checking possible values for B2:

B2=6 -> A12={1,4}, A6=21 - 5 - 10 = 6 which is impossible.

B2=4 implies that one of A12 is odd which is impossible.

B2=3 -> A12={2,4}, A6=5, B6=1, B34={2,6} which is impossible.

B2=2 -> A1=2, A2=6, A6=3, B34={3,6}, B1=5, B6=1, C3=2 leaving no place for a 2 in Column D.

Hence we have established that D6=3 and B5=2.

The rest of the solution is routine.

B34={3,6}, D5=5, D4=2

There is an Xwing on value 4 in rows 1,2 columns BD. So A1, A2 C1,C2, E1, E2, F1, F4 are all ~4.

ETC.

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clm wrote:

[Merry Christmas and a Happy New 2024 for everyone. ]

Thanks clm and wishing all the same as well!

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pnm wrote:

someone sent me a difficult 6x6 from Simon Tatham's website, and it _is_ difficult

(my solver rates it slightly above the regular difficult 6x6 on the site (!))

I started solving it, but am momentarily stuck (would like to find a solving path not

involving trial-and-error )

Anyone have any ideas?

Hi, Patrick.

Step 1: to determine that "4-" is [1,5] but not [2,6].

Applying the parity rule, since "30x" is even and "6x" is odd we arrive to the conclusion that the sum of "2:" and "2:" in the right hand corner (columns e and f) must be odd, which means that one of them must be even [2,4] and the other odd ([1,2] or [3,6]).

The sum of "30x" and "6x" is always 17 ([2,3,5] plus [1,6] or [1,5,6] plus [2,3]).

Now, suppose "4-" is [2,6], the two division cages must be [2,4] and [3,6]. As a consequence, the three cages have a sum of 8 + 6 + 9 = 23. Now we have: 18 + 17 + 23 = 58, so "1-" in f2-f3 = 5, that is, [2,3], which is impossible since no more 2's can be located in columns e or f. Then,

The two division cages, "2:" in the right corner must be [2,4] and [3,6] with a sum of 15. And then, 18 + 17 + 6 + 15 = 56, thus

We find very interesting conclusions from here, for instance, "a3" = 5; "7+" can't be [2,5] and "60x" must be [1,2,5,6] or [1,3,4,5] since [2,2,3,5] is now impossible. The 5 of "30x" is in d5, otherwise b5 = 5, but [1,2,6] or [1,3,4] would inhibit at the same time [2,4] or [3,6] for cage "2:" in e6-f6. So,

Let's continue with the analytical solution. The 5 in column e must be in e2 (since there is a 5 in b1 or c1). This means that d1 + e1 + d2 = 12. The possibilities, without any 5, are [3,3,6] or [2,4,6] for those positions, but the first one is not possible because it would inhibit "30x"; thus [2,4,6].

The cage "24x" must be [2,3,4] or [1,4,6] since [2,2,6] is not possible now. Consequently, this cage has a 4 and, since there is another 4 in [2,4,6], "1-" in b1-c1 must be [5,6] and not [4,5].

The rest is as follows:

Then

Finally, "2:" in e5-f5 = [3,6] with

And "2:" in e6-f6 = [2,4] with

The full analytical solution we have arrived is:

356421

241653

532164

463215

124536

615342

Comment: The puzzle is quite difficult. I believe this is because of the presence of four division cages "2:". In general, the division cages, as the subtraction cages, increase the level of difficulty.

Merry Christmas and a Happy New 2024 for everyone.

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I started solving it, but am momentarily stuck (would like to find a solving path not

involving trial-and-error )

Anyone have any ideas?

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Not being under time pressure certainly makes a difference to my clarity of thought and I managed to solve it, albeit with a little bit of trial and error. The message to myself is not to leave puzzles until the last minute. Sometimes however, life gets in the way and the other lesson learned is not to let it stress me out if I don’t solve ALL of a particular day’s puzzles.

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