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Killer Calcudoku: no operators, no cages
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Posted on: Sat Dec 17, 2011 3:26 pm

Posts: 700
Joined: Fri May 13, 2011 6:51 pm
Killer Calcudoku: no operators, no cages
This is a sample, a 5x5 (1 to 5) without cages and without operators, I have named this "invention" "Killer Calcudoku" due to the, in some way, similarity to the "killer sudoku". Only the results of the cages are shown. The solver should distribute the numbers, draw the cages (tip: consider the position of the results, that is, we may draw lines in the top and in the left of any of those "results") and define the operator. I think the solution is unique but I can be wrong (I am not sure if any software can manage this at this moment).

Posted on: Sat Dec 17, 2011 5:47 pm

Posts: 422
Joined: Fri May 13, 2011 2:43 am
Re: Killer Calcudoku: no operators, no cages
I believe it's unique. Very interesting variation! I've never thought of it before.

Posted on: Sat Dec 17, 2011 10:28 pm

Posts: 700
Joined: Fri May 13, 2011 6:51 pm
Re: Killer Calcudoku: no operators, no cages
sneaklyfox wrote:
I believe it's unique. Very interesting variation! I've never thought of it before.

Thank you for your time and comments, this type of puzzle could be perhaps quite difficult, even a 4x4 (a typical 4x4 with standard arithmetic operations is generally solved, let's say by a medium player, in a few minutes - less than a minute for an advanced player) could require some time of analysis.

Posted on: Sun Dec 18, 2011 5:06 am

Posts: 175
Joined: Fri May 13, 2011 2:11 am
Re: Killer Calcudoku: no operators, no cages
Should we assume the numbers are in the top left corner of the cage as normally?

Regardless, wow this seems hard. I'm going to go work it soon, since it seems fun.

Posted on: Sun Dec 18, 2011 9:57 am

Posts: 700
Joined: Fri May 13, 2011 6:51 pm
Re: Killer Calcudoku: no operators, no cages
starling wrote:
Should we assume the numbers are in the top left corner of the cage as normally?

Regardless, wow this seems hard. I'm going to go work it soon, since it seems fun.

In this example it is enough that the cell with the result shown be in the top or in the leftmost position of the cage (10 results = 10 cages logically), however that's a very good point to be considered and agreed as a rule since, for instance, it could be imagined a 5-cell cage with a shape of a cross with the result in the bottom cell, in the central cell or even in the righmost cell and this would make the puzzles more difficult like in the "Nurikabe" puzzles where you have many ways to connect the lines. In this initial 5x5 example any cage is formed "surrounding" the cell with the result with the top and the left segments of that cell until all segments and lines in the grid are connected consistently creating all the necessary cages and with a unique solution for the puzzle. It would be very interesting to know if a different arrangement of the cages (each including inside one result regardless of the position) can be found.

Posted on: Sun Dec 18, 2011 10:02 pm

Posts: 422
Joined: Fri May 13, 2011 2:43 am
Re: Killer Calcudoku: no operators, no cages
clm wrote:
starling wrote:
Should we assume the numbers are in the top left corner of the cage as normally?

Regardless, wow this seems hard. I'm going to go work it soon, since it seems fun.

In this example it is enough that the cell with the result shown be in the top or in the leftmost position of the cage (10 results = 10 cages logically), however that's a very good point to be considered and agreed as a rule since, for instance, it could be imagined a 5-cell cage with a shape of a cross with the result in the bottom cell, in the central cell or even in the righmost cell and this would make the puzzles more difficult like in the "Nurikabe" puzzles where you have many ways to connect the lines. In this initial 5x5 example any cage is formed "surrounding" the cell with the result with the top and the left segments of that cell until all segments and lines in the grid are connected consistently creating all the necessary cages and with a unique solution for the puzzle. It would be very interesting to know if a different arrangement of the cages (each including inside one result regardless of the position) can be found.

I believe in Patrick's puzzles, the result is usually shown first in the topmost cell and then the leftmost cell (if more than one "topmost" cell. In other words, for the 5-cell cage in the shape of a cross, the result would be shown in the head of the cross. In clm's puzzle, the result would be in the head (top) OR in the left arm.

Posted on: Sun Dec 18, 2011 10:09 pm

Posts: 422
Joined: Fri May 13, 2011 2:43 am
Re: Killer Calcudoku: no operators, no cages
clm wrote:
It would be very interesting to know if a different arrangement of the cages (each including inside one result regardless of the position) can be found.

I found at least one alternate arrangement disregarding the position of the result.

Posted on: Mon Dec 19, 2011 12:54 am

Posts: 700
Joined: Fri May 13, 2011 6:51 pm
Re: Killer Calcudoku: no operators, no cages
sneaklyfox wrote:
clm wrote:
starling wrote:
Should we assume the numbers are in the top left corner of the cage as normally?

Regardless, wow this seems hard. I'm going to go work it soon, since it seems fun.

In this example it is enough that the cell with the result shown be in the top or in the leftmost position of the cage (10 results = 10 cages logically), however that's a very good point to be considered and agreed as a rule since, for instance, it could be imagined a 5-cell cage with a shape of a cross with the result in the bottom cell, in the central cell or even in the righmost cell and this would make the puzzles more difficult like in the "Nurikabe" puzzles where you have many ways to connect the lines. In this initial 5x5 example any cage is formed "surrounding" the cell with the result with the top and the left segments of that cell until all segments and lines in the grid are connected consistently creating all the necessary cages and with a unique solution for the puzzle. It would be very interesting to know if a different arrangement of the cages (each including inside one result regardless of the position) can be found.

I believe in Patrick's puzzles, the result is usually shown first in the topmost cell and then the leftmost cell (if more than one "topmost" cell. In other words, for the 5-cell cage in the shape of a cross, the result would be shown in the head of the cross. In clm's puzzle, the result would be in the head (top) OR in the left arm.

You are right, the Patrick's arrangement would have been this (but I thought it was going to be easier since the 3 in d1 is isolated):

Anyway here is the solution for both arrangements, the original

and the one in the hypothesis of the Patrick's arrangement (which is the same solution though I confess I have not studied much this second one) and I am impatient for your alternate arrangement disregarding the position of the result. However, now I am thinking that it would be perhaps better to let free the position of the result (in any cell of the cage, like in the example of the cross, with 5 possible positions) in order to make the puzzle more difficult and attractive:

Posted on: Mon Dec 19, 2011 4:12 am

Posts: 422
Joined: Fri May 13, 2011 2:43 am
Re: Killer Calcudoku: no operators, no cages
The alternate that I found is not much different.

Posted on: Mon Dec 19, 2011 7:02 pm

Posts: 700
Joined: Fri May 13, 2011 6:51 pm
Re: Killer Calcudoku: no operators, no cages
sneaklyfox wrote:
The alternate that I found is not much different.

Very interesting, thank you, it´s really a quite different solution, this demonstrates that the position of the operator is not irrelevant. Now we could think inversely: if we take, for instance, a 5x5 difficult among the past Patrick's puzzles (we know they have a unique solution) and we remove from it the operators and the cages, keeping only the results, so converting it in a "killer calcudoku" we may ask: are there different solutions now? (I have tried with one and initially I have not found an alternate solution). In this point we have two ways: with the results in the Patrick's positions or with the results regardless of the position.

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