sheldolina wrote:

I couldn't solve the ... 9x9 difficult ...

With respect to the yesterdays’s 9x9 puzzle, I was thinking in your comment and thought that the following notes could be useful to see that this calcudoku is, in fact, quite easy, if we apply the analysis, the basic rules.

Green: The 5 of row 9 (in this case with a 2) to g8. Then “24x” = [1,4,6] >>> a8 = 1, a9 = 7 (unique).

Purple: “18144x” = [4,7,8,9,9], [6,6,7,8,9] so it does not contain a 3 >>> e9 = 3, h9 = 9.

The 9 of column i to i9 (unique) so we are left with [4,7,8] for this cage.

Addition rule to columns h and i: “84x” (+) + h7 + h8 = 30. Since “84x” = [1,2,6,7] (16) or [1,3,4,7] (15) (obviously [2,2,3,7] not considered due to a double 2 and there is a 2 in “10x”) >>> h7 + h8 = 14 or 15, neither can be done including a 4, so g8 = 4, h7-h8 = [7,8] and then “84x” = [1,3,4,7].

Brown: The 9 of column e to e7 >>> d7 = 7.

Addition rule to rows 3 and 4: a + b + c (cells d3, e4, h4, respectively) = 12 but a and b are even so c is even, so c = h4 = 2, h5 = 5. Now a + b = 10 but [1,9], [3,7], [4,6] or [5,5] are invalid thus [2,8] >>> d3 = 2, e4 = 8. Additionally “13+” = [4,9] (unique) >>> c2 = 4, d2 = 8.

Light blue: First b9 = 4, c9 = 1, d9 = 6.

Now looking to the pair e8-f8 (sum of 11), since [2,9], [3,8], [4,7] are not valid >>> e8 = 6, f8 = 5, e1-e2 = [1,2] >>> f1-f2 = [6,8].

Also the 9 of column c to c3 >>> b3 = 5.

Addition rule to columns f and g: g1 + g2 = 12 = [3,9].

Red: Directly c8 = 2 (unique for this cell). Now c1 cann’t be a 5 (a 4 and a 6 in column d) so c7 = 5, c1 = 6 (or, inversely, c7 cann’t be a 6 due to g8 = 4, d2 = 8 that would make imposible the cage “0-”). As a consequence, d8 = 3, d1 = 5.

Addition rule to rows 7, 8 and 9 (sum of 135): g7 + i7 = 3 >>> g7 = 2, i7 = 1.

Addition rule to rows 5 and 6: a6 + b6 = 3 >>> a6 = 2, b6 = 1. Now “5-” = [2,7] ([3,8] is not possible due to two 8’s in rows 1 and 2).

Addition rule to columns a and b: a1 + a2 = 14 >>> [5,9] with a1 = 9, a2 = 5.

The rest can be quickly finished (not represented in the graphic): The 5 of column i to i4 (unique) >>> i3 = 4; now h1-h2 = [1,4] and i1-i2 = [3,7]. Other: d6 = 4, d5 = 9. Also c5 = 8, c6 = 7. And, i.e., the 6 of column i to i6, or, f2 = 6, f1 = 8, etc. …

(The official solution because in the future will not be available

:)