# Another Colombian Sudoku

Solve the Sudoku on the left, where the usual rules apply.

The dots outside the board on the right indicate how many cells in the corresponding column or row of that board contain precisely the same digit as is to be found in the same cell of the solved Sudoku on the left.

• the right one is no sudoku, maybe use "grid" or table Commented Apr 19 at 7:57

Here is the answer; blue is the same, orange is different:

Here's a gif of how I solved the puzzle, in reverse (using this site, hosted via Giphy); green is used to designate a pair where one will be orange and the other will be blue:

Nice puzzle!

Here's my go at it:

I started by marking all the known data to the right hand square, then solved it using sudoku rules (out of three 4s in a column, at least two must be wrong, etc), and ended up with this easyish sudoku:

A more complete write-up coming up as soon as I have the time.

We will use chess notation. Columns a to f from left to right and row 1 to 6 from bottom to top. In the board, digits with <> are givens, digits with ** are derived digits. No candidates will be used. HS means hidden single, FH means full house.

                                              .   .        .            .
.   .        .   .        .   .
.   .        .   .        .   .
.   .        .   .   .    .   .   .
.   .        .   .   .    .   .   .
.--------------------------------------.  .--------------------------------------.
9 |*9*  .   .  | .   .   .  | .  *5*  .  |  | 9   7   2  | 1   7   3  | 2   5   5  | . . . . .
8 | .  <7>  .  | .  <2>  .  | .  <4>  .  |  | 8   7   6  | 3   8   5  | 6   9   6  | . . . .
7 | .   .   .  | .   .   .  | .   .   .  |  | 5   4   5  | 4   3   1  | 2   5   6  |
|------------+------------+------------|  |------------+------------+------------|
6 |*8* *2*  .  | .   .   .  |*5* *9* *6* |  | 8   2   2  | 4   9   4  | 5   9   6  | . . . . . .
5 |*4* <9>  .  | .  <5>  .  |*3* <1>  .  |  | 4   9   2  | 4   5   3  | 3   9   6  | . . . .
4 | .   .   .  | .   .   .  | .   .   .  |  | 9   7   7  | 2   3   7  | 6   4   2  |
|------------+------------+------------|  |------------+------------+------------|
3 | .  *8*  .  | .   .   .  | .  *6*  .  |  | 5   8   6  | 7   1   3  | 2   6   2  | . . . . . . .
2 |*3* <1>  .  | .  <4>  .  |*9* <8>  .  |  | 3   4   2  | 2   6   4  | 9   3   3  | . . .
1 | .   .   .  | .   .   .  | .  *7*  .  |  | 5   4   6  | 2   9   3  | 5   7   8  | . . .
'--------------------------------------'  '--------------------------------------'
a   b   c    d   e   f    g   h   i       a   b   c    d   e   f    g   h   i


. Column b: We have at least 4 mismatches [(7)b9,(4)b2,(7)b4,one of (4)b17] and two matching digits [(7)b8, (9)b5]. Since we must have exactly 5 matching digits (and thus 4 not matching), we need 3 additional matching digits and no mismatches in that column.

=> b6=2, b3 = 8, and (4)b17. (*)

. Row 6, we have at least 3 mismatches [one of (4)df6, one of (2)bc6, one of (9)eh6]. Since we must have 6 matches, it follows that: a6 = 8, g6=5, i6=6

. Column a: we have at least 4 mismatches [(8)a8,(9)a4,two of (5)a13] and need exactly 5 matches, so a9=9, a5=4, a2=3.

. Row 8: we have at least 6 mismatches [(4)b2,one of (2)cd2,(6)e2,(4)f2,(3)h2,(3)i2], due to the givens or derived digits. Since we must have 3 matches, it follows that g2=9

. Column g: we have at least 5 mismatches [two of (2)g379, one of (6)g48, one of (5)g16]. Since we must have 5 matches at that column, it follows that g5=3.

. Column h: we have 5 mismatches: h2,h4,h5,h8 [due to the givens] and one of (5)h79 [board 2] So, no more mismatch is possible in this column: h9=5, h6=9, h3=6, h1 = 7.

                                              .   .        .            .
.   .        .   .        .   .
.   .        .   .        .   .
.   .        .   .   .    .   .   .
.   .        .   .   .    .   .   .
.--------------------------------------.  .--------------------------------------.
9 |*9*  .   .  | .   .   .  | .  *5*  .  |  | 9   7   2  | 1   7   3  | 2   5   5  | . . . . .
8 | .  <7>  .  | .  <2>  .  | .  <4>  .  |  | 8   7   6  | 3   8   5  | 6   9   6  | . . . .
7 | .   .   .  | .   .   .  | .  *3*  .  |  | 5   4   5  | 4   3   1  | 2   5   6  |
|------------+------------+------------|  |------------+------------+------------|
6 |*8* *2*  .  | .   .   .  |*5* *9* *6* |  | 8   2   2  | 4   9   4  | 5   9   6  | . . . . . .
5 |*4* <9>  .  | .  <5>  .  |*3* <1>  .  |  | 4   9   2  | 4   5   3  | 3   9   6  | . . . .
4 | .   .   .  | .   .   .  | .  *2* *4* |  | 9   7   7  | 2   3   7  | 6   4   2  |
|------------+------------+------------|  |------------+------------+------------|
3 |*5* *8*  .  | .  *1* *3* |*4* *6* *2* |  | 5   8   6  | 7   1   3  | 2   6   2  | . . . . . . .
2 |*3* <1>  .  | .  <4>  .  |*9* <8> *5* |  | 3   4   2  | 2   6   4  | 9   3   3  | . . .
1 | .   .   .  | .   .   .  |*1* *7* *3* |  | 5   4   6  | 2   9   3  | 5   7   8  | . . .
'--------------------------------------'  '--------------------------------------'
a   b   c    d   e   f    g   h   i       a   b   c    d   e   f    g   h   i


Now the only place for 3 at column h is h7=3, and h4=2.

Row 3: we need 7 matches and we already have at least two mismatches: one of (2)rgi3 and (6)c3. Therefore, a3=5, e3=1, and f3=3.

Only one place for 3 at box h2 (the "center" of the box): i1=3. Only one place for 1 at box h2: g1=1. Only one place for 5 at box h2: i2 = 5.

Column i: (6)i6 is the only match so far. We need one more and there is only one possible (due to derived digits at i1,i2,h4,h9,i6): i3=2 => g3=4 => i4=4.

                                                  .        .
.        .
.        .
.        .       .
ok  .        .   ok  .    ok  ok  ok
.--------------------------------------.  .--------------------------------------.
9 |*9*  .   .  |*1* *7*  .  |*2* *5*  .  |  | 9   7   2  | 1   7   3  | 2   5   5  | . . . . .
8 | .  <7>  .  |*3* <2> *5* |*6* <4>  .  |  | 8   7   6  | 3   8   5  | 6   9   6  | . . . .
7 | .   .   .  | .   .   .  |*7* *3*  .  |  | 5   4   5  | 4   3   1  | 2   5   6  |
|------------+------------+------------|  |------------+------------+------------|
6 |*8* *2*  .  |*4*  .   .  |*5* *9* *6* |  | 8   2   2  | 4   9   4  | 5   9   6  | ok
5 |*4* <9>  .  | .  <5>  .  |*3* <1> *7* |  | 4   9   2  | 4   5   3  | 3   9   6  | ok
4 |*7*  .   .  | .   .   .  |*8* *2* *4* |  | 9   7   7  | 2   3   7  | 6   4   2  |
|------------+------------+------------|  |------------+------------+------------|
3 |*5* *8* *9* |*7* *1* *3* |*4* *6* *2* |  | 5   8   6  | 7   1   3  | 2   6   2  | ok
2 |*3* <1> *7* | .  <4>  .  |*9* <8> *5* |  | 3   4   2  | 2   6   4  | 9   3   3  | . . .
1 | .   .   .  |*5* *9* *8* |*1* *7* *3* |  | 5   4   6  | 2   9   3  | 5   7   8  | . . .
'--------------------------------------'  '--------------------------------------'
a   b   c    d   e   f    g   h   i       a   b   c    d   e   f    g   h   i


Column d: we have at least 4 mismatches [one of (2)d12, (4)d7, one of (4)d56,(2)d4]. Since we must have exactly 5 matches, it follows that d9=1,d8=3,d3=7 (=>c3=9). Also, (2)d12 and (4)d56 must hold, and due to (4)a5, we must have (4)d6. Rows 3, 5 and 6 matching conditions are fulfilled. In column a, there is only one possible place for 7 (due to <7>b8,7h1): a4=7. => i5=7, h4=8, c2=7.

. Column e: we have 5 mismatches at e2,e4,e6,e7,e8 and need two additional matches (already have e3,e5 matching, so e1=9, e9=7. => g7=7 (due to <7>b8,7 at i5,e9). => g9=2 (only place possible for 2 in column g, due to <2>e8), g8=6 (FH) Matching conditions are fulfilled in column, g,h,i.

Row 8: we need an additional matching (b8,d8,g8 are matches) and the only possible place (due to 8a6,6g8) is f8=5. => d1=5, f1=8 (HS).

                                                  .
.
.
.
ok  .        ok  ok  ok   ok  ok  ok
.--------------------------------------.  .--------------------------------------.
9 |*9*  .   .  |*1* *7* *4* |*2* *5* *8* |  | 9   7   2  | 1   7   3  | 2   5   5  | ok
8 | .  <7>  .  |*3* <2> *5* |*6* <4>  .  |  | 8   7   6  | 3   8   5  | 6   9   6  | ok
7 | .   .   .  | .   .   .  |*7* *3*  .  |  | 5   4   5  | 4   3   1  | 2   5   6  |
|------------+------------+------------|  |------------+------------+------------|
6 |*8* *2*  .  |*4*  .   .  |*5* *9* *6* |  | 8   2   2  | 4   9   4  | 5   9   6  | ok
5 |*4* <9>  .  | .  <5> *2* |*3* <1> *7* |  | 4   9   2  | 4   5   3  | 3   9   6  | ok
4 |*7*  .   .  | .   .   .  |*8* *2* *4* |  | 9   7   7  | 2   3   7  | 6   4   2  |
|------------+------------+------------|  |------------+------------+------------|
3 |*5* *8* *9* |*7* *1* *3* |*4* *6* *2* |  | 5   8   6  | 7   1   3  | 2   6   2  | ok
2 |*3* <1> *7* |*2* <4> *6* |*9* <8> *5* |  | 3   4   2  | 2   6   4  | 9   3   3  | ok
1 | .   .   .  |*5* *9* *8* |*1* *7* *3* |  | 5   4   6  | 2   9   3  | 5   7   8  | . . .
'--------------------------------------'  '--------------------------------------'
a   b   c    d   e   f    g   h   i       a   b   c    d   e   f    g   h   i


Row 2: We need 3 matches, having already the ones at a2,g2. Due to 7d3, we must have d2=2=> f2=6, f5=2 (due to 2h4,b6,d2).

Row 9: We have all needed matches at a9,d9,e9,g9,h9. We have a hidden pair (36)bc9, due to 3f3,i1, and 6 i6,f2, so in that row the only place for digit 4 (due to the mentioned hidden pair and (4) i4) is f9=4 => i9=8.

                                              ok  ok       ok  ok  ok   ok  ok  ok
.--------------------------------------.  .--------------------------------------.
9 |*9*  .   .  |*1* *7* *4* |*2* *5* *8* |  | 9   7   2  | 1   7   3  | 2   5   5  | ok
8 | .  <7>  .  |*3* <2> *5* |*6* <4>  .  |  | 8   7   6  | 3   8   5  | 6   9   6  | ok
7 | .   .   .  | .   .   .  |*7* *3*  .  |  | 5   4   5  | 4   3   1  | 2   5   6  |
|------------+------------+------------|  |------------+------------+------------|
6 |*8* *2*  .  |*4*  .   .  |*5* *9* *6* |  | 8   2   2  | 4   9   4  | 5   9   6  | ok
5 |*4* <9>  .  | .  <5> *2* |*3* <1> *7* |  | 4   9   2  | 4   5   3  | 3   9   6  | ok
4 |*7*  .   .  | .   .   .  |*8* *2* *4* |  | 9   7   7  | 2   3   7  | 6   4   2  |
|------------+------------+------------|  |------------+------------+------------|
3 |*5* *8* *9* |*7* *1* *3* |*4* *6* *2* |  | 5   8   6  | 7   1   3  | 2   6   2  | ok
2 |*3* <1> *7* |*2* <4> *6* |*9* <8> *5* |  | 3   4   2  | 2   6   4  | 9   3   3  | ok
1 |*6* *4* *2* |*5* *9* *8* |*1* *7* *3* |  | 5   4   6  | 2   9   3  | 5   7   8  | ok
'--------------------------------------'  '--------------------------------------'
a   b   c    d   e   f    g   h   i       a   b   c    d   e   f    g   h   i


Row 1: We have matching at e1,h1 and need one more at a1,b1, or c1. At c1 is not possible due to the restriction at column c in the second board [no matching], in a1 is not possible due to (5)a3, so b1=4 => a1=6, c1= 2. This fulfills the matching conditions of Row 1.

Row 8: We have at least 5 mismatches [a8,e8,i8,one of (6)cg8] and 2 matches [b8,d8].

                                              ok  ok  ok   ok  ok  ok   ok  ok  ok
.--------------------------------------.  .--------------------------------------.
9 |*9* *6* *3* |*1* *7* *4* |*2* *5* *8* |  | 9   7   2  | 1   7   3  | 2   5   5  | ok
8 |*1* <7> *8* |*3* <2> *5* |*6* <4> *9* |  | 8   7   6  | 3   8   5  | 6   9   6  | ok
7 |*2* *5* *4* |*6* *8* *9* |*7* *3* *1* |  | 5   4   5  | 4   3   1  | 2   5   6  |
|------------+------------+------------|  |------------+------------+------------|
6 |*8* *2* *1* |*4* *3* *7* |*5* *9* *6* |  | 8   2   2  | 4   9   4  | 5   9   6  | ok
5 |*4* <9> *6* |*8* <5> *2* |*3* <1> *7* |  | 4   9   2  | 4   5   3  | 3   9   6  | ok
4 |*7* *3* *5* |*9* *6* *1* |*8* *2* *4* |  | 9   7   7  | 2   3   7  | 6   4   2  |
|------------+------------+------------|  |------------+------------+------------|
3 |*5* *8* *9* |*7* *1* *3* |*4* *6* *2* |  | 5   8   6  | 7   1   3  | 2   6   2  | ok
2 |*3* <1> *7* |*2* <4> *6* |*9* <8> *5* |  | 3   4   2  | 2   6   4  | 9   3   3  | ok
1 |*6* *4* *2* |*5* *9* *8* |*1* *7* *3* |  | 5   4   6  | 2   9   3  | 5   7   8  | ok
'--------------------------------------'  '--------------------------------------'
a   b   c    d   e   f    g   h   i       a   b   c    d   e   f    g   h   i


At column 1, a7=2 (HS), a8=1 (FH), i7=1 (HS), i8=9 (FH), c8=8 (FH), d5=8 (HS),c5=6(FH), b9=6 (due to HT(689)def8) and 6c5) => c9=3 (FH) => b4=3 (HS), e5=3 (HS), f6=7 (HS), c6=1 (FH), c4=5 (FH), b7=5 (HS), c7=4 (FH). We not in passing that the non-matching condition on column c is fulfilled. Also, e7=8 (HS), d7=6 (HS), f7=9 (FH). Finally, f4=1 (FH), e4=6 (FH), d4=9 (FH).