Initial grid

  +-------------+
6 | . 1 . . . . |
5 | 5 4 . . . . |
4 | . . 2 1 . . |
3 | . . 5 2 3 1 |
2 | . . . 5 . . |
2 | . . . 3 . 4 |
  +-------------+ Latin Squares
    a b c d e f
    

Update 1 (Oct 14, 2026)

After basics

  ,-------------------------------,
6 | 236  1    36  *4    256  2356 |
5 | 5    4    13  *6    12   23   |
4 | 36   35   2    1   *4    356  |
3 |*4   *6    5    2    3    1    |
2 | 1236 23 * 4    5    126  236  |
1 | 126  25   16   3    1256 4    |
  '-------------------------------'
    a    b    c    d    e    f

The hint is to find a way to show
that (6)f6 must be false. For that
I used the weakness in row 5, column c
    

Update 2 (Oct 16, 2026)

Either (6=23)b2.f2 - (3)a2 = (36)a4.f4 is true,
or the spoiler (3)a6 is true, but in this
case (6)c6 is true, so: -6 f6

  ,-------------------------------,
6 | 236  1    36  *4    256  235  |
5 | 5    4    13  *6    12   23   |
4 | 36   35   2    1   *4    356  |
3 |*4   *6    5    2    3    1    |
2 | 1236 23 * 4    5    126  236  |
1 | 126  25   16   3    1256 4    |
  '-------------------------------'
    a    b    c    d    e    f

Now, the new strong link (6)f2=(6)f4 can be
used for an elimination in the column f.
    

Update 3 (Oct 18, 2026)
    
After the previous step (S-wing) we arrive at

  ,-------------------------------,
6 | 236  1    36  *4    256  235  |
5 | 5    4    13  *6    12   23   |
4 | 36   35   2    1   *4    356  |
3 |*4   *6    5    2    3    1    |
2 | 1236 23 * 4    5    126  26   |
1 | 126  25   16   3    1256 4    |
  '-------------------------------'
    a    b    c    d    e    f

Now a second (well hidden) wing type exists
eliminating (2)a1, with a Naked Pair that
eliminates 1,6 e1.

After this move, only one additional move needs
to be found.
    

Update 4 (Oct 20, 2026)

Finally, the newly produced strong link
(1)e2 = (1)e5 creates another wing that
eliminates (6)e2, solving the puzzle.

  ,-------------------------------,
6 | 236  1    36  *4    256  235  |
5 | 5    4    13  *6    12   23   |
4 | 36   35   2    1   *4    356  |
3 |*4   *6    5    2    3    1    |
2 | 1236 23 * 4    5    12-6 26   |
1 | 16   25   16   3    25   4    |
  '-------------------------------'
    a    b    c    d    e    f
    
    

Initial position (and last move played):

White: Ke1, Bc1, Bf1, Rh1, Ng6, Qh5, a2, b2, c4, d2, e3, g2, h2.
Black: Ke8, Qa1, Ra8, Rh8, Nb8, Ng8, Bc8, Bf8, a7, b7, c7, f6, h7.

(Black's last move: 10... Qxa1)

Update 1 (Oct 14, 2026)

After 11.Nxh8+ Kd8!

[after 11... Kd7? 12.Be2! Nh6 13.0-0 and black seems to be in big trouble]

12.Nf7+ Ke7 13.Qxh7!

Interesting position! How to continue ?

Update 2 (Oct 17, 2026)

I considered two possibilities for black:

(A) 13... Ke8

(B) 13... Bf5

Both options lead to complex position with many ways
to continue for both sides.

. As a sample, in option (A):

14.Be2! Qxc1+ 15.Kf2 Qxh1 16.Bh5 looks very dangerous!

How should black continue in this variation ?

Update 3 (Oct 18, 2026)

Other interesting variations for analysis

for this (open ended problem) are

. In option (A): 14.Qxg8 Qxc1+ 15.Kf2 Nc6
  and now, how should white continue ?

. In option (B): 14.Qxf5 Qxc1 + 15.Kf2 Kxf7
  and now, how should white continue ?