## Fun puzzle. So many methods to solve. No CHAINS required.

Post puzzles for others to solve here.
Wapati wrote:This has lots of Turbots or lots of ERs, depending on the path you take?

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` *------------------------------------------------------* | 2     8     9   | 1     5     3    | 6     4     7   | | 7     6     1   | 9     4     2    | 5     3     8   | | 5     3     4   | 6     7     8    | 9     1     2   | |-----------------+------------------+-----------------| | 9     4     5   | 3     26    67   | 8     27    1   | | 6     27    8   | 24    1     47   | 3     9     5   | | 3     1     27  | 8     9     5    | 247   267   46  | |-----------------+------------------+-----------------| | 4     279   267 | 5     26    169  | 127   8     3   | | 8     5     267 | 24    3     1469 | 1247  267   469 | | 1     29    3   | 7     8     469  | 24    5     469 | *------------------------------------------------------*`

[r9c2]=2=[r7c3]=6=[r8c3](-6-[r8c8])=2=[r8c7]-2-[r9c7]=2=[r9c2],

and so r9c2=2 solving the puzzle.

Carcul
Carcul

Posts: 724
Joined: 04 November 2005

carcul wrote:[r9c2]=2=[r7c3]=6=[r8c3](-6-[r8c8])=2=[r8c7]-2-[r9c7]=2=[r9c2],

and so r9c2=2 solving the puzzle.

Now I'm totally lost... From where did you get the stong links [r9c2]=2=[r7c3] and [r8c3]=2=[r8c7]? I'm sorry, but I don't know any good portuguese phrase to express my confusion...

RW
RW
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Wapati wrote:I had troubles with this one. I do like it when URs are required rather than shortcuts!

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` *-------------------------------------------------------* | 46    7     456  | 1     8     456 | 9     2     3    | | 369   8     356  | 56    2     569 | 1     47    47   | | 49    1     2    | 3     49    7   | 8     5     6    | |------------------+-----------------+------------------| | 5     269   4689 | 7     46    1   | 3     48    24   | | 16    26    7    | 48    3     268 | 45    9     125  | | 134   23    348  | 9     5     24  | 6     1478  1247 | |------------------+-----------------+------------------| | 2     3569  369  | 48    7     689 | 45    16    159  | | 7     4     69   | 56    1     569 | 2     3     8    | | 8     569   1    | 2     469   3   | 7     46    459  | *-------------------------------------------------------*`

[r1c3]=5=[r2c3]=3=[r2c1](-3-[r6c1])=9=[r2c6]-9-[r78c6]-{Nice Loop:
[r5c6]-2-[r5c12]-1-[r6c1]-4-[r6c6]-2-[r5c6]}-2-[r578c6]-5,6-[r1c6](-4-
-[r1c3])-4-[r1c1]-6-[r1c3],

implying that r1c3<>4,6, which solves the puzzle (using an additional trivial step).

Carcul
Carcul

Posts: 724
Joined: 04 November 2005

carcul wrote:[r1c3]=5=[r2c3]=3=[r2c1](-3-[r6c1])=9=[r2c6]-9-[r78c6]-{Nice Loop:
[r5c6]-2-[r5c12]-1-[r6c1]-4-[r6c6]-2-[r5c6]}-2-[r578c6]-5,6-[r1c6](-4-
-[r1c3])-4-[r1c1]-6-[r1c3],

implying that r1c3<>4,6, which solves the puzzle (using an additional trivial step).

Trivial step... I see 2 URs to solve it after that. Here's a shorter one that solves it immediately, could be done even without applying the x-wing first:

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` *-------------------------------------------------------*  | 46    7     456  | 1     8     456 | 9     2     3    |  | 369   8     356  | 56    2     569 | 1     47    47   |  | 49    1     2    | 3     49    7   | 8     5     6    |  |------------------+-----------------+------------------|  | 5     269   4689 | 7     46    1   | 3     48    24   |  | 16    26    7    | 48    3     268 | 45    9     125  |  | 134   23    348  | 9     5     24  | 6     1478  1247 |  |------------------+-----------------+------------------|  | 2     3569  369  | 48    7     689 | 45    16    159  |  | 7     4     69   | 56    1     569 | 2     3     8    |  | 8     569   1    | 2     469   3   | 7     46    459  |  *-------------------------------------------------------*`

r2c1=3 => r2c6=9 => r3c5=4 => r7c4=4 => r5c7=4 => r4c3=4

=> BUG-lite in r1c36, r2c34, r8c46 => r2c1<>3

or perhaps you prefer the nice loop approach (let's see if I can get this right):
[r2c1]=9=[r2c6]-9-[r3c5](-4-[r4c5])-4-[r9c5]=4=[r7c4]-4-[r7c7]=4=[r5c7]-4-[r4c89]=4=[r4c3]-4-[r1c3]-{BUG-lite: r1c36,r2c34,r8c46}-56-[r2c3]-3-[r2c1]

=> r2c1<>3

RW
RW
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Carcul wrote:
Ocean wrote:Even simpler is this XY-wing:

Why simpler? The number of links is the same.

Yea, right. The the same number of links. Your forcing chain is elegant logic that works in both directions. Still, to me the xy-wing appears simpler, but it's maybe a matter of taste.

Why simpler?

The xy-wing gives the logical equation: "x=7=>x<>7" (same in both directions).
Ergo: "x<>7".

The other chain gives - forward direction: "y<>7=>y<>9".
In the reverse direction: "y=9=>y=7".
(These two are equivalent).
From these we can conclude "y<>9".

The first case (xy-wing) is simple and obvious (at least after having seen the xy-wing in other puzzles now and then, once having accepted general proofs for it's validity, etc). The second case is a bit more complicated - so complicated that the equations may not stay in my memory long enough to carry out the deductions, unless I am specially trained for it. (It is still nice and elegant, although harder to spot).
Ocean

Posts: 442
Joined: 29 August 2005

Ocean wrote:The first case (xy-wing) is simple and obvious (at least after having seen the xy-wing in other puzzles now and then, once having accepted general proofs for it's validity, etc). The second case is a bit more complicated - so complicated that the equations may not stay in my memory long enough to carry out the deductions, unless I am specially trained for it. (It is still nice and elegant, although harder to spot).

Again, "obvious", "hard to spot", "nice", "elegant", are all subjective issues. For me, there is absolutely no difference between the two, because they both have the same number of links. They are equal nice loops in light of the bilocation/bivalue plot. Also, I don't know what you mean by "equations". Don't forget that this is not mathematics.
No offense, by I think that some of you people complicate things so much, by wanting to give a more "scientific" (or "beautifull", or "socially more cute", I don't know) character to the deductions, and I see how that hinder people to see things as clear as crystal.

RW wrote:Trivial step... I see 2 URs to solve it after that.

Look more carefully. There is a direct deduction.

RW wrote:Here's a shorter one that solves it immediately, could be done even without applying the x-wing first:

Yes, I also spoted that one, but I finded the one I posted more interesting (because of the trivial step).

RW wrote:Now I'm totally lost... From where did you get the stong links [r9c2]=2=[r7c3] and [r8c3]=2=[r8c7]?

I will leave that as another riddle.

Carcul
Carcul

Posts: 724
Joined: 04 November 2005

Wapati wrote:ER to the rescue. APE can be used, apparently, but I don't know it. Fortunately there is a work around using grouped x and ER. phew!

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` *---------------------------------------------------------* | 7      4      13 | 135    6      8   | 9      2      35 | | 15     6      8  | 9      237    123 | 157    137    4  | | 9      135    2  | 135    347    134 | 157    6      8  | |------------------+-------------------+------------------| | 125    15     6  | 23     8      347 | 12457  137    9  | | 125    8      7  | 6      34     9   | 1245   13     35 | | 3      9      4  | 12     5      17  | 6      8      27 | |------------------+-------------------+------------------| | 6      37     9  | 4      1      23  | 8      5      27 | | 4      137    13 | 8      23     5   | 27     9      6  | | 8      2      5  | 7      9      6   | 3      4      1  | *---------------------------------------------------------*`

[r6c9]-2-[r7c9]-7-[r7c2]-3-[r8c3]=3=[r1c3]=1=[r1c4]-1-[r6c4]-2-[r6c9],

and so r6c9<>2 solving the puzzle.

Carcul
Last edited by Carcul on Wed Oct 18, 2006 5:33 am, edited 1 time in total.
Carcul

Posts: 724
Joined: 04 November 2005

carcul wrote:
RW wrote:Now I'm totally lost... From where did you get the stong links [r9c2]=2=[r7c3] and [r8c3]=2=[r8c7]?

I will leave that as another riddle.

Okay, guess I have to counter with another riddle... Shorter solution for the puzzle I solved in my last post:
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` *-------------------------------------------------------*  | 46    7     456  | 1     8     456 | 9     2     3    |  | 369   8     356  | 56    2     569 | 1     47    47   |  | 49    1     2    | 3     49    7   | 8     5     6    |  |------------------+-----------------+------------------|  | 5     269   4689 | 7     46    1   | 3     48    24   |  | 16    26    7    | 48    3     268 | 45    9     125  |  | 134   23    348  | 9     5     24  | 6     1478  1247 |  |------------------+-----------------+------------------|  | 2     3569  369  | 48    7     689 | 45    16    159  |  | 7     4     69   | 56    1     569 | 2     3     8    |  | 8     569   1    | 2     469   3   | 7     46    459  |  *-------------------------------------------------------*`

We have either r7c2=3 or r1c1=6. However:

[r7c2]=3=[r7c3]-3-[r2c3]=3=[r2c1]=9=[r3c1]=4=[r3c5]-4-[r1c6]=4=[r6c6]-4-[r6c1]=4=[r1c1]

So r7c2=3 which solves the puzzle.

carcul wrote:Consider the cells r1c7/r1c8/r8c8 and r8c7. As the first three where given as clues, r8c7 cannot be "2", otherwise we would have an unavoidable set. So, r8c7=7 and the puzzle is solved.

I'm afraid that elimination cannot be correct. There are other given clues in column 8 and 9 as well, so it cannot be a reverse BUG-light and there are other given instances of digits 2 and 9, so it cannot be a reverse BUG. Or did you have anything else in mind? There can of course be unavoidable sets in the solution, as long as there is given clues in them. The reverse uniqueness technique spots sets that must have an unavoidable counterpart, and works only if there is no givens in the counterparts of the spotted set.

RW
RW
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RW wrote:I'm afraid that elimination cannot be correct.(...)There can of course be unavoidable sets in the solution, as long as there is given clues in them. The reverse uniqueness technique spots sets that must have an unavoidable counterpart, and works only if there is no givens in the counterparts of the spotted set.

Yes, you are obviously right. Thanks.

RW wrote:We have either r7c2=3 or r1c1=6. However:

[r7c2]=3=[r7c3]-3-[r2c3]=3=[r2c1]=9=[r3c1]=4=[r3c5]-4-[r1c6]=4=[r6c6]-4-[r6c1]=4=[r1c1]

So r7c2=3 which solves the puzzle.

Very good. However, here's an even shorter solution for that puzzle:

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` *-------------------------------------------------------*  | 46    7     456  | 1     8     456 | 9     2     3    |  | 369   8     356  | 56    2     569 | 1     47    47   |  | 49    1     2    | 3     49    7   | 8     5     6    |  |------------------+-----------------+------------------|  | 5     269   4689 | 7     46    1   | 3     48    24   |  | 16    26    7    | 48    3     268 | 45    9     125  |  | 134   23    348  | 9     5     24  | 6     1478  1247 |  |------------------+-----------------+------------------|  | 2     3569  369  | 48    7     689 | 45    16    159  |  | 7     4     69   | 56    1     569 | 2     3     8    |  | 8     569   1    | 2     469   3   | 7     46    459  |  *-------------------------------------------------------* `

If r6c1 is not "3" then we would have Two Incompatible Loops:

-3-[r6c1]-{TILA: [r5c6]-2-[r5c12]-1-[r6c1]-4-[r6c6]-2-[r5c6]; [r1c6]-4-
-[r3c5]=4=[r3c1]-4-[r6c1]-1-[r5c1]-6-[r1c1]-4-[r1c6]}.

So, r6c1 must be "3" and the puzzle is solved.

Carcul
Carcul

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Then mine is the shortest

We have either r9c5=9 or r6c1=1
But: r6c6=2 => r1c6=4 (=> r1c1=6 => r5c1=1) => r3c5=9
So r6c6=4 which solves the puzzle.
ravel

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Ravel wrote:Then mine is the shortest

No it's not. Your solution uses the same number of cells as mine. So they are both the shortest.

Carcul
Carcul

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[Edited:] Withdrawn
Last edited by daj95376 on Wed Oct 18, 2006 12:32 pm, edited 2 times in total.
daj95376
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daj95376 wrote:
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`Multi-Colors on <2> => [r6c7],[r7c2],[r7c7],[r8c3],[r8c8]<>2 This leaves [r7c3]|[r9c2]=2 in [b7] Follow with a Naked Pair and Multi-Colors on <7> to get a cascade of Singles.`

I'm aware of the coloring possibility, but I think carcul's intention was to submit a solution that solves the puzzle in one step, getting around the multicoloring... And your coloring still doesn't explain the mysterious [r8c3]=2=[r8c7]... "É muita areia para a minha camioneta."

RW
RW
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RW wrote:I'm aware of the coloring possibility, but I think carcul's intention was to submit a solution that solves the puzzle in one step, getting around the multicoloring... And your coloring still doesn't explain the mysterious [r8c3]=2=[r8c7]

Yes, that's true.

RW wrote:"É muita areia para a minha camioneta."

Very nice expression. So I think that for you, after Daj's possibility, "ficou tudo em águas de bacalhau".

Carcul
Carcul

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Joined: 04 November 2005

Here is a pretty good one.
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`6 . 8 | . . 9 | . . .9 1 . | . . . | . 4 .. . 5 | 7 . . | . . .---------------------. 2 6 | . . 7 | . . 45 . . | . . . | . . .7 . 1 | . . . | 5 . .---------------------. . . | 4 . 1 | 8 . 2. . . | . . 3 | . 5 .. . . | 5 9 . | . 1 6`
wapati
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