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Step by step solution of an 9x9
http://www.calcudoku.org/forum/viewtopic.php?f=3&t=120
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Author:  jomapil  [ Wed Nov 30, 2011 6:35 pm ]
Post subject:  Step by step solution of an 9x9

I beg your goodwill to the presentation of this puzzle. It's my first one
and also the first contact with the tools used. Anyway I thank for your critiques,
opinions, alternative steps and suggestions.

I limited the most the text and pretended that the "step by step" was exactly
a "step by step" exhaustive and complete for other begginers (save the obvious).


I advise the eventual interested to draw the diagram and to accompany, writing
everything on the paper.

And now, as almost always, I'm sorry for my English ( To write this text
I consulted the dictionary 8 times ).

Image

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1) green
2) yellow: "192*"=[4,6,8]
3) brown: "1008x"=[2,7,8,9]
4) blue
5) grey: "252*"=[1,4,7,9]

Image

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6) green: Analysing row 6 : "48*"<<>>7, "2880x"<<>>7 --> e1=7.
"280*"=[1,5,7,8],[2,4,5,7].
"48#"=[2,3,8],[3,4,4].
Analysing column 8 --> h6=9.
Analysing row 6 --> b6=7.


7) yellow: h5=1 --> c5=8,c4=1.
"4-"(a4)=[2,3,9],[1,4,9]. c4=1 -->"4-"=[2,3,9].
"2-"=[2,4],[3,5]. a6=2,3,4,8, i6=2,3,4,8.


8) brown: "2880x"=[1,5,8,8,9],[2,4,5,8,9].


9) "6-"=[1,7],[2,8]. h7=8 and i7=1 --> "2880x"<<>>[1,5,8,8,9]

--> "2880x"=[2,4,5,8,9].

10) There should be a 8 in the column h of "192x" and in the column i of "2880x",

i.e. "192x"(hhhh) and "2880x"(iiii) or vice versa. Then, all the other 8s of those

columns must disappear. So h9<>8, i9<>8 --> g9=8.


Image

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11) In the column i it lacks (1,3).

So "4-"(i2)=[x,1],[x,3] --> "4-"(i2)=[1,5],[3,7]

and "4-"(i2)(+)=[6,10].


(h+++)+(i+++)= 45+45= 90. Knowing the sum of all the cages of the two columns,

"2880x"(+)=2+4+5+8+9=28 and so on, we have:

85 + "4-"(i2)(+) + h2 - g9=90 --> h2 + "4-"(i2)(+) = g9 +5 "4-"(i2)(+)=[6,10].

If (4-)(i2)(+) = 6 --> h2=7 unique possibility

If (4-)(i2)(+) = 10 --> h2=3 impossible

After this h2=7, g2=5, [f1,g1]=[2,4].


Image

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12) green: h9=2, i9=7, h7=5

e5=5 --> f5=3, d5<>3 --> d5=[2,4] --> d6=[2,3,8],

e6=[2,4,8], h1=[6,8].



13) yellow: i4=6 --> h3=[4,8] --> h1=6.

i1=3 --> "4-"(i2)=[1,5] --> i2=1, i3=5.

a=[7], b=[7] --> e1=7.

"16+"=[7,1,8],[7,2,7],[7,3,6],[7,4,5] __> e2=3,f2=6, a2=9, b2=8, d2=2

-- > "48x"=[4,3,4], a6=[2,8], i6=[2,8]

g8=[4,7] --> g1=2, f1=4, b1=1, a1=8.



Image

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14) green: a6=2, i6=8, i7=[2,4], a4=3, b4=2, b8=5, b9=4,

f9=1, f8=[4,7] --> c8=2, c7=7.


15) yellow: "112x"=[1,2,7,8] --> d3=7, e3=1, e4=8 --> f4=4,

f3=8 --> g4=7, g8=4, f8=7.


f=[...,2,8,9,...] --> "0-"=[2,9], f7=8, f6=2, i7=4,

"252x"=[1,2,3,6,7] --> a6=2, b7=3, a7=6, a8=1, a4=3, e8=6.



To complete now the puzzle, it is very simple.
The hardest of this puzzle is the number 11). If anyone uses a different method
I wolud like to know.

Author:  honkhonk  [ Wed Nov 30, 2011 7:57 pm ]
Post subject:  Re: Step by step solution of an 9x9

Quite a walkthrough jomapil! It's nice to have look at other solver's strategies...

About step 11,

You write column i lacks [1,3], this is true but also the columns h and i lack a 6 (image 2). Based on the information in that image 6 can only be in either h1 or i1, hence "9+"=[6,3]. Thus "4-"<> [7,3] but only "4-"=[1,5].

If I have correctly followed your walkthrough, does this help?

Author:  jomapil  [ Thu Dec 01, 2011 12:55 am ]
Post subject:  Re: Step by step solution of an 9x9

Good point and thank you, Honkhonk.
It's good to see other solutions, because they teaches us more tricks.
I hope more variations on my solution.

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