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 ).
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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]
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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.
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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].
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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.
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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.
