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 8x8 medium 9/6 
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Posted on: Thu Sep 06, 2018 1:51 am




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Joined: Mon Sep 25, 2017 2:43 am
Post 8x8 medium 9/6
Did anyone else find this puzzle really difficult? I got a chunk of stuff across the middle really easily, knew all three right hand columns down to at worst two possibilities each (like the 1- in the upper right is 4-3 in some order), and the same along the bottom. But then I totally stalled and had to guess and check for like half an hour to get it. Was this really a medium puzzle? What was I missing?


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Posted on: Thu Sep 06, 2018 8:31 am




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Joined: Thu May 12, 2011 11:51 pm
Post Re: 8x8 medium 9/6
My experience was similar.

Edit: I wonder if this one had more subtractions than usual, especially in the top three rows, and if that contributed to the difficulty. My trial and error key came in determining whether 5 went int the 1st square of row 8 or in the 8+ cell next to it. There were only 103 solvers 2 weeks ago because it was a subscriber only puzzle.


Last edited by sjs34 on Thu Sep 06, 2018 1:40 pm, edited 1 time in total.



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Posted on: Thu Sep 06, 2018 10:44 am




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Joined: Tue Mar 01, 2016 10:03 pm
Post Re: 8x8 medium 9/6
I also found it quite tricky. I abandoned it last night and started again from scratch this morning, but it took me nearly 20 minutes to solve and a certain amount of trial and error.

I think the difficulty level is reflected by the relatively low number of people who have solved this puzzle - I think I was the 125th. I went back over the last month of Thursday medium 8x8s and the number of solvers was typically around 500, although the one from two weeks ago only had 107 solvers.


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Posted on: Fri Sep 07, 2018 5:24 am




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Joined: Mon Sep 25, 2017 2:43 am
Post Re: 8x8 medium 9/6
I tried it again - there's a little help on the top row. There was a 9+ and a 0-, so those add up to some odd number. That means the sum of the three numbers on the right are the top row. So those have to be 3 odd numbers or one odd and two even, and some of those use up the numbers that would have to go in the 0-. That at least narrowed down the guessing I had to do.


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Posted on: Fri Sep 07, 2018 5:24 pm




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Joined: Sun Nov 03, 2013 10:28 pm
Post Re: 8x8 medium 9/6
Yep, it didn't feel like a medium puzzle at all.


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Posted on: Fri Sep 07, 2018 5:36 pm




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Joined: Thu May 12, 2011 11:58 pm
Post Re: 8x8 medium 9/6
Below is the puzzle for reference.

I checked the numbers, this one was defintely at the "high end" of medium (a certain number
that's calculated during generation is set to be between 5000 and 25000, for this puzzle it was 23000+)
(often it's around 10000)

Image


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Posted on: Sat Sep 08, 2018 10:21 am




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Joined: Sun Jan 31, 2016 7:52 am
Post Re: 8x8 medium 9/6
It does seem more difficult than usual for a medium puzzle.

I did as much as I could without doing anything in the top left part of the puzzle, then I added the cages in rows 5,6 and 7, this meant cell a6 can be solved and then the rest of the puzzle is straight forward.


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Posted on: Sat Sep 08, 2018 11:11 am




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Joined: Fri May 13, 2011 6:51 pm
Post Re: 8x8 medium 9/6
sjs34 wrote:
My experience was similar.

Edit: I wonder if this one had more subtractions than usual, especially in the top three rows, and if that contributed to the difficulty. My trial and error key came in determining whether 5 went int the 1st square of row 8 or in the 8+ cell next to it. There were only 103 solvers 2 weeks ago because it was a subscriber only puzzle.


In my opinion that's exactly what happens. For instance, we know that in a KS the difficulty level increases if the size of the cages increase, that is, if you have cages with a big number of cells (though being additions, the number of possibilities increase). The subtraction cages operate in a similar way in a Calcudoku. The number of possibilities, in both types of puzzle, is proportional to the difficulty, since they require more analysis and more time to solve the puzzle. So a quick look to the puzzle gives you an initial idea of the difficulty.

The subtraction cages have a bigger number of possibilities (combinations), depending on the "measure" of the cage, and inversely to this "measure", i.e., a 2-cell "5-" cage (let's call it of "measure" 5), in an 8x8, has three possible combinations: [1,6], [2,7] and [3,8], while a 2-cell "1-" cage, in the same puzzle, has seven possible combinations: [1,2], [2,3], [3,4], [4,5], [5,6], [6,7] and [7,8], being, for a 2-cell cage, the number of possibilities equal to the "distance" between the size of the puzzle and the "measure" of the cage (8 - 5 = 3 in the first case and 8 - 1 = 7 in the second case).

A 3 cell L-shape "0-" cage, in an 8x8 (fm 1 to 8) has sixteen possible combinations: [1,1,2], [2,2,4], [3,3,6], [4,4,8], [1,2,3], [1,3,4], [1,4,5], [1,5,6], [1,6,7], [1,7,8], [2,3,5], [2,4,6 ], [2,5,7], [2,6,8], [3,4,7] and [3,5,8] (BTW, a 3-cell L-shape "1-" cage, in the same puzzle, would have twelve possible combinations).

A multiplication cage has in general fewer possibilities, i.e., a 3-cell L-shape "72x" cage, in the same puzzle, has only three possible combinations: [3,3,8], [3,4,6] and [2,6,6].

In the puzzle we are considering we have a total of 11 subtraction cages, mainly concentrated in the 5 leftmost columns, and three of them are 3 cell L-shape "0-" cages. Additionally, the 3-cell in-line "0-" cage in the upper row has "initially" twelve possible combinations.


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Posted on: Sat Sep 08, 2018 12:29 pm




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Joined: Sun Jan 31, 2016 7:52 am
Post Re: 8x8 medium 9/6
While it is true that the size of the cages and the type of operator can indicate how difficult a puzzle is, this can be negated by the number of possible combinations being reduced as the puzzle solution progresses. In this puzzle I did not give any thought to the two 0- cages in the top 3 rows until there was enough of the puzzle solved that the answer for each cell was clear.


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Posted on: Sat Sep 08, 2018 1:59 pm




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Joined: Thu May 12, 2011 11:58 pm
Post Re: 8x8 medium 9/6
I could reduce the upper limit on the 8x8 medium somewhat,
so puzzles like these won't appear again?


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