The New Sudoku Players' Forum

[jco]

Hi!

Just an observation: this sudoku-X puzzle (SE = 7.6) proposed by philvo here can be solved without pencilmarks.

Code: Select all

+-------+-------+
| . . . | . . . |
| . . 4 | . . . |
+-------+-------+
| . . . | . . 5 |
| . . . | . . 3 |
+-------+-------+
| . . . | . . . |
| . . . | 6 2 . |
+-------+-------+ X

EDIT (Feb 3, 2025): included hidden partial solution

Hidden Text: Show

Due to (6)d1, we have (6)e3|e4 and (6)f5|f6,
and (6)a6|b5|c4.

If f5=6, then a6=6
(otherwise (6)c4, (6)b6, (6)c2 and no 6 in the second diagonal),
and there is no "6" at c4,a1 or a2, so (6)b2|c2.
We cannot have (6)b2

Code: Select all

+--------+-------+
| A .  . | . . . | 6
| . .  4 | . . A | 5
+--------+-------+
| . .  -A| . . 5 | 4
| . .  . | . . 3 | 3
+--------+-------+
| . A  -A| . . . | 2
| . .  . | 6 2 . | 1
+--------+-------+
  a b  c   d e f   Sudoku-X

because there would be no 6 at box 3.
So, under the assumption f5=6, we must
have (6)c2

Code: Select all

+--------+-------+
| A .  . | . . . | 6
| . .  4 | . . A | 5
+--------+-------+
| . .  -A| . . 5 | 4
| . .  . | . . 3 | 3
+--------+-------+
| . -A A | . . . | 2
| . .  . | 6 2 . | 1
+--------+-------+
  a b  c   d e f   Sudoku-X


however this implies that there is
no 6 at the second diagonal (/).
So, we must have f6=6 and
f5=2.

EDIT (Feb 15, 2026): corrected old standing typo (f5 instead of a5) and missing text in the (hidden) partial solution.

[jco]

This post aims at drawing attention to corrections for a long standing typo and missing text that made the previous post difficult to follow.
Following the observation (already given at the previous post) that this sudoku-X puzzle (SE = 7.6) proposed by philvo here can be solved without pencilmarks,

Code: Select all

+-------+-------+
| . . . | . . . |
| . . 4 | . . . |
+-------+-------+
| . . . | . . 5 |
| . . . | . . 3 |
+-------+-------+
| . . . | . . . |
| . . . | 6 2 . |
+-------+-------+ X

a complete solution is given (hidden)

Hidden Text: Show

Due to (6)d1, we have (6)e3|e4 and (6)f5|f6, and (6)a6|b5|c4.

If f5=6, then a6=6
(otherwise (6)c4, (6)b6, (6)c2 and no 6 in the second diagonal),
and there is no "6" at c4,a1 or a2, so (6)b2|c2.
We cannot have (6)b2

Code: Select all

+--------+-------+
| A .  . | . . . | 6
| . .  4 | . . A | 5
+--------+-------+
| . .  -A| . . 5 | 4
| . .  . | . . 3 | 3
+--------+-------+
| . A  -A| . . . | 2
| . .  . | 6 2 . | 1
+--------+-------+
  a b  c   d e f   Sudoku-X

because there would be no 6 at box 3.
So, under the assumption f5=6, we must
have (6)c2

Code: Select all

+--------+-------+
| A .  . | . . . | 6
| . .  4 | . . A | 5
+--------+-------+
| . .  -A| . . 5 | 4
| . .  . | . . 3 | 3
+--------+-------+
| . -A A | . . . | 2
| . .  . | 6 2 . | 1
+--------+-------+
  a b  c   d e f   Sudoku-X


however this implies (again) that there is no 6 at the second diagonal (/).
So, we must have f6=6 and f5=2. Then, (6)a5|b5 and (6)b5|c4.

We cannot have A=6 at a5, because

Code: Select all

+--------+--------+
| . .  . | . . *6*| 6
| A .  4 | . . *2*| 5
+--------+--------+
| . .  A | . .  5 | 4
| . .  . | . .  3 | 3
+--------+--------+
| . .  . | . .  . | 2
| . .  . | 6 2  . | 1
+--------+--------+
  a b  c   d e  f   Sudoku-X

that implies c4=A leaving no place
for a 6 at box 5 [bottom-left].

So, b5=6. Also, from (6)f6, (6)b5, the only place for 6 at column c is c2=6.

Code: Select all

+-----------+---------+
| .   .   . | .  . *6*| 6
| .  *6*  4 | .  . *2*| 5
+-----------+---------+
| .   .   . | .  .  5 | 4
| .   .   . | .  .  3 | 3
+-----------+---------+
| .   .  *6*| .  .  . | 2
| .   .   . | 6  2  . | 1
+-----------+---------+
  a   b   c   d  e  f   Sudoku-X


Now, we notice that A=2 at d4 is not possible
because it implies A=2 at a2, leaving
no place for A=2 at the main diagonal.
So, d3=2, and c6=2.

Code: Select all

+-----------+---------+
| .   .  *2*| .  . *6*| 6
| .  *6*  4 | .  . *2*| 5
+-----------+---------+
| .   .   . | .  .  5 | 4
| .   .   . |*2* .  3 | 3
+-----------+---------+
| .   .  *6*| .  .  . | 2
| .   .   . | 6  2  . | 1
+-----------+---------+
  a   b   c   d  e  f   Sudoku-X


Now, the only place for a "4" at the diagonal
a6-f1 is f1=4 [since (3|5)e2], so f2=1.

Code: Select all

+-----------+---------+
| .   .  *2*| .  . *6*| 6
| .  *6*  4 | .  . *2*| 5
+-----------+---------+
| .   .   . | .  .  5 | 4
| .   .   . |*2* .  3 | 3
+-----------+---------+
| .   .  *6*| .  . *1*| 2
| .   .   . | 6  2 *4*| 1
+-----------+---------+
  a   b   c   d  e  f   Sudoku-X


The only place for a "2" at diagonal
a1-f6 is b2=2, so a2=4, and a4=2,
and a3=6, e4=6.

Code: Select all

+-----------+---------+
| .   .  *2*| .  . *6*| 6
| .  *6*  4 | .  . *2*| 5
+-----------+---------+
|*2*  .   . | . *6* 5 | 4
|*6*  .   . |*2* .  3 | 3
+-----------+---------+
|*4* *2* *6*| .  . *1*| 2
| .   .   . | 6  2 *4*| 1
+-----------+---------+
  a   b   c   d  e  f   Sudoku-X


Looking for placing "4" at diagonal a1-f6,
the only place is d4=4, so e3=1, e6=4, b3=4,

Code: Select all

+-----------+-----------+
| .   .  *2*| .  *4* *6*| 6
| .  *6*  4 | .   .  *2*| 5
+-----------+-----------+
|*2*  .   . |*4* *6*  5 | 4
|*6* *4*  . |*2* *1*  3 | 3
+-----------+-----------+
|*4* *2* *6*| .   .  *1*| 2
| .   .   . | 6   2  *4*| 1
+-----------+-----------+
  a   b   c   d   e   f   Sudoku-X

c3 = 5, b1=5

Code: Select all

+-----------+-----------+
| .   .  *2*| .  *4* *6*| 6
| .  *6*  4 | .   .  *2*| 5
+-----------+-----------+
|*2*  .   . |*4* *6*  5 | 4
|*6* *4* *5*|*2* *1*  3 | 3
+-----------+-----------+
|*4* *2* *6*| .   .  *1*| 2
| .  *5*  . | 6   2  *4*| 1
+-----------+-----------+
  a   b   c   d   e   f   Sudoku-X

a1=1 (only in diagonal a1-f6),
c1=3, c4=1, b4=3, b6=1, d5=1.

Code: Select all

+-----------+-----------+
| .  *1* *2*| .  *4* *6*| 6
| .  *6* <4>|*1*  .  *2*| 5
+-----------+-----------+ 
|*2* *3* *1*|*4* *6* <5>| 4
|*6* *4* *5*|*2* *1* <3>| 3
+-----------+-----------+
|*4* *2* *6*| .   .  *1*| 2
|*1* *5* *3*|<6> <2> *4*| 1
+-----------+-----------+
  a   b   c   d   e   f   Sudoku-X


Now, due to (5)c3, we must have e5=3,
d6=5, d2=3, e2=5, a6=3, a5=5.

Code: Select all

  +-----------+-----------+
6 |*3* *1* *2*|*5* *4* *6*|
5 |*5* *6* <4>|*1* *3* *2*|
  +-----------+-----------+ 
4 |*2* *3* *1*|*4* *6* <5>|
3 |*6* *4* *5*|*2* *1* <3>|
  +-----------+-----------+
2 |*4* *2* *6*|*3* *5* *1*|
1 |*1* *5* *3*|<6> <2> *4*|
  +-----------+-----------+
  a   b   c   d   e   f   Sudoku-X