The New Sudoku Players' Forum

[Papy]

If my solver doesn't use recursive
can I try to solvc with or only human solver can compite?
Papy

[ravel]

Any good and human readable solution is appreciated.

[Ocean]

Hello Ocean,

The Explainer Rating 10.0 is probably a new "record" - provided that puzzle has enough steps. Maybe a suitable challenge for you, Maria?

I solved this ER10.0 puzzle last friday. I don't know if I should post it, spoiling the fun for the other manual solvers?

Congratulations, Maria!
Posting the solution is just fine. The challenge for other potential solvers will be to find simpler/shorter solutions.

Somehow disappointingly, it was not the hardest puzzle in terms of solving strategy. My solution has gone quite straightforward. It also didn't needed more than 10 contradictions, so that's equal to the #07/18 puzzle with ER9.9. (...)
Greetings, Maria

... also thanks for your evaluation of difficulty.

Will be interesting to see how many steps Ravel's program needs, for this and the other 31 recently submitted puzzles.

[maria45]

Concerning the Explainer ranking:

I don't know how it is that the ER10.0 is rated so high. I have copied here the more difficult solution techniques of the ER10.0 puzzle and the new #2 in the same list:

ER10.0
6 x Forcing Chain
3 x Cell Forcing Chains
6 x Region Forcing Chains
3 x Dynamic Cell Forcing Chains
26 x Dynamic Contradiction Forcing Chains
8 x Dynamic Region Forcing Chains
4 x Dynamic Contradiction Forcing Chains (+)

ER9.9 (.....1..2.1..3..4.5..6.......4.....1.7..8..3.2.....6..9....2.......4..7...35..8..)
9 x Forcing Chain
2 x Nishio Forcing Chains
3 x Cell Forcing Chains
11 x Region Forcing Chains
1 x Dynamic Cell Forcing Chains
5 x Dynamic Region Forcing Chains
19 x Dynamic Contradiction Forcing Chains
9 x Dynamic Contradiction Forcing Chains (+)

So, in terms of the most difficult technique, the Dynamic Contradiction Forcing Chains(+), the 9.9er puzzle is way harder than the 10.0er.

Only if you sum up all contradiction forcing chains, the ER9.9 gets 28, the ER10.0 gets 30.

I'd like to predict that Ravels program would need more steps with the 9.9er here.

[r.e.s.]

maria45,

The ER10 puzzle has one particular move that by itself is rated 10.0 (just step through the Explainer solving path to find it) -- whereas all the moves in the ER9.9 puzzles are individually rated 9.9 or less. (For ERs I think it's generally true that an x-rated puzzle has at least one x-rated move in the reported solution path.)

It seems somewhat of a problem to compare the difficulty of
(1) a solution path that has a number of 9.9-rated moves but no 10-rated move, and
(2) a solution path that has fewer 9.9-rated moves than (1) but instead has one or a few 10-rated moves.

Also note that issues like how hard is the very first move or first placement can also affect these judgements (e.g. the ER9.9 puzzle you mention is a nice <pearl>, but the ER10 puzzle is not.

EDIT: Removed question about ER>10 (it's explained earlier in this thread) , rewording.

[ronk]

The ER10 puzzle has one particular move that by itself is rated 10.0

The candidate grid at that point is ...

Code: Select all

.....1..2.1..2..3.4..5.......4.....6.7..3..1.8.....9..5....8.......1..7...64..5..

 3679  5689  3789  | 36789 46789 1     | 4678  45689 2
 679   1     5789  | 6789  2     4679  | 4678  3     4589
 4     23689 2389  | 5     6789  3679  | 17    689   1789
-------------------+-------------------+------------------
 1239  2359  4     | 1789  578   279   | 37    258   6
 269   7     59    | 2689  3     469   | 248   1     458
 8     2356  13    | 1267  456   2467  | 9     245   37
-------------------+-------------------+------------------
 5     2349  17    | 23679 679   8     | 12346 2469  1349
 239   23489 2389  | 2369  1     5     | 23468 7     489
 17    2389  6     | 4     79    237   | 5     289   1389

[edit: r2c9 candidates corrected as per r.e.s.]

Sudoku Explainer's next move is r4c4<>7. Can anyone find an alternate move?

[ronk]

Double post deleted. Must have clicked "quote" instead of "edit".

[r.e.s.]

ronk,

In your grid, I think r2c9 should have only the candidates 4589 (you wrote 45789); otherwise, I get the same grid.

For reference (copy/paste to an editor), here's the Explainer's description of the next move (rated 10.0), which concludes r4c4<>7 ...

Dynamic Contradiction Forcing Chains

With this rule, we will prove the two following assertions:
If R4C4 contains the value 7, then R8C9 must contain the value 9
If R4C4 contains the value 7, then R8C9 cannot contain the value 9
Because the same assumption yields t[w]o contradictory results, we can conclude that the assumption is false, that is, R4C4 cannot contain the value 7.

Each assertion is proved by a different chain of simple rules. The chains can be dynamic, which means that the conclusions of multiple sub-chains must be combined in some cases.
The details of each chain are given below. Use the view selector below the grid to switch between the graphical illustrations of the two different chains.

Chain 1:
If R4C4 contains the value 7, then R8C9 cannot contain the value 9 (View 1):
(1) If R4C4 contains the value 7, then R4C4 cannot contain the value 1 (the cell can contain only one value)
(2) If R4C4 does not contain the value 1, then R6C4 must contain the value 1 (only remaining possible position in the block)
(3) If R6C4 contains the value 1, then R6C3 cannot contain the value 1 (the value can occur only once in the row)
(4) If R6C3 does not contain the value 1, then R7C3 must contain the value 1 (only remaining possible position in the column)
(5) If R7C3 contains the value 1, then R7C7 cannot contain the value 1 (the value can occur only once in the row)
(6) If R7C7 does not contain the value 1, then R3C7 must contain the value 1 (only remaining possible position in the column)
(7) If R3C7 contains the value 1, then R3C7 cannot contain the value 7 (the cell can contain only one value)
(8) If R7C3 contains the value 1 (4), then R7C3 cannot contain the value 7 (the cell can contain only one value)
(9) If R4C4 contains the value 7 (initial assumption), then R7C4 cannot contain the value 7 (the value can occur only once in the column)
(10) If R7C4 does not contain the value 7 and R7C3 does not contain the value 7 (8), then R7C5 must contain the value 7 (only remaining possible position in the row)
(11) If R7C5 contains the value 7, then R3C5 cannot contain the value 7 (the value can occur only once in the column)
(12) If R4C4 contains the value 7 (initial assumption), then R6C6 cannot contain the value 7 (the value can occur only once in the block)
(13) If R4C4 contains the value 7 (initial assumption), then R6C4 cannot contain the value 7 (the value can occur only once in the block)
(14) If R6C4 does not contain the value 7 and R6C6 does not contain the value 7 (12), then R6C9 must contain the value 7 (only remaining possible position in the row)
(15) If R6C9 contains the value 7, then R3C9 cannot contain the value 7 (the value can occur only once in the column)
(16) If R3C9 does not contain the value 7, R3C5 does not contain the value 7 (11) and R3C7 does not contain the value 7 (7), then R3C6 must contain the value 7 (only remaining possible position in the row)
(17) If R3C6 contains the value 7, then R3C6 cannot contain the value 3 (the cell can contain only one value)
(18) If R3C6 does not contain the value 3, then R1C4 must contain the value 3 (only remaining possible position in the block)
(19) If R1C4 contains the value 3, then R1C1 cannot contain the value 3 (the value can occur only once in the row)
(20) If R4C4 does not contain the value 1 (1), then R4C1 must contain the value 1 (only remaining possible position in the row)
(21) If R4C1 contains the value 1, then R4C1 cannot contain the value 3 (the cell can contain only one value)
(22) If R4C1 does not contain the value 3 and R1C1 does not contain the value 3 (19), then R8C1 must contain the value 3 (only remaining possible position in the column)
(23) If R8C1 contains the value 3, then R8C1 cannot contain the value 2 (the cell can contain only one value)
(24) If R4C1 contains the value 1 (20), then R4C1 cannot contain the value 2 (the cell can contain only one value)
(25) If R4C1 does not contain the value 2 and R8C1 does not contain the value 2 (23), then R5C1 must contain the value 2 (only remaining possible position in the column)
(26) If R5C1 contains the value 2, then R5C7 cannot contain the value 2 (the value can occur only once in the row)
(27) If R5C7 does not contain the value 2, then R9C8 cannot contain the value 2 (Pointing: Cells R4C8,R6C8: 2 of block in column)
(28) If R4C1 contains the value 1 (20), then R9C1 cannot contain the value 1 (the value can occur only once in the column)
(29) If R9C1 does not contain the value 1, then R9C1 must contain the value 7 (only remaining possible value in the cell) (30) If R9C1 contains the value 7, then R9C5 cannot contain the value 7 (the value can occur only once in the row)
(31) If R9C5 does not contain the value 7, then R9C5 must contain the value 9 (only remaining possible value in the cell) (32) If R9C5 contains the value 9, then R9C8 cannot contain the value 9 (the value can occur only once in the row)
(33) If R9C8 does not contain the value 9 and R9C8 does not contain the value 2 (27), then R9C8 must contain the value 8 (only remaining possible value in the cell)
(34) If R9C8 contains the value 8, then R4C8 cannot contain the value 8 (the value can occur only once in the column)
(35) If R4C4 contains the value 7 (initial assumption), then R4C4 cannot contain the value 8 (the cell can contain only one value)
(36) If R4C4 does not contain the value 8 and R4C8 does not contain the value 8 (34), then R4C5 must contain the value 8 (only remaining possible position in the row)
(37) If R4C5 contains the value 8, then R3C5 cannot contain the value 8 (the value can occur only once in the column)
(38) If R6C3 does not contain the value 1 (3), then R6C3 must contain the value 3 (only remaining possible value in the cell)
(39) If R6C3 contains the value 3, then R3C3 cannot contain the value 3 (the value can occur only once in the column)
(40) If R3C3 does not contain the value 3 and R3C6 does not contain the value 3 (17), then R3C2 must contain the value 3 (only remaining possible position in the row)
(41) If R3C2 contains the value 3, then R3C2 cannot contain the value 8 (the cell can contain only one value)
(42) If R3C2 contains the value 3 (40), then R3C2 cannot contain the value 2 (the cell can contain only one value)
(43) If R3C2 does not contain the value 2, then R3C3 must contain the value 2 (only remaining possible position in the block)
(44) If R3C3 contains the value 2, then R3C3 cannot contain the value 8 (the cell can contain only one value)
(45) If R9C8 contains the value 8 (33), then R3C8 cannot contain the value 8 (the value can occur only once in the column)
(46) If R3C8 does not contain the value 8, R3C3 does not contain the value 8 (44), R3C2 does not contain the value 8 (41) and R3C5 does not contain the value 8 (37), then R3C9 must contain the value 8 (only remaining possible position in the row)
(47) If R3C9 contains the value 8, then R3C9 cannot contain the value 9 (the cell can contain only one value)
(48) If R1C4 contains the value 3 (18), then R1C4 cannot contain the value 9 (the cell can contain only one value)
(49) If R9C5 contains the value 9 (31), then R1C5 cannot contain the value 9 (the value can occur only once in the column) (50) If R9C5 contains the value 9 (31), then R3C5 cannot contain the value 9 (the value can occur only once in the column) (51) If R3C6 contains the value 7 (16), then R3C6 cannot contain the value 9 (the cell can contain only one value)
(52) If R3C6 does not contain the value 9, R3C5 does not contain the value 9 (50), R1C5 does not contain the value 9 (49) and R1C4 does not contain the value 9 (48), then R2C9 cannot contain the value 9 (Pointing: Cells R2C4,R2C6: 9 of block in row)
(53) If R9C1 does not contain the value 1 (28), then R9C9 must contain the value 1 (only remaining possible position in the row)
(54) If R9C9 contains the value 1, then R9C9 cannot contain the value 3 (the cell can contain only one value)
(55) If R4C4 contains the value 7 (initial assumption), then R4C7 cannot contain the value 7 (the value can occur only once in the row)
(56) If R4C7 does not contain the value 7, then R4C7 must contain the value 3 (only remaining possible value in the cell)
(57) If R4C7 contains the value 3, then R7C7 cannot contain the value 3 (the value can occur only once in the column)
(58) If R4C7 contains the value 3 (56), then R8C7 cannot contain the value 3 (the value can occur only once in the column)
(59) If R8C7 does not contain the value 3, R7C7 does not contain the value 3 (57) and R9C9 does not contain the value 3 (54), then R7C9 must contain the value 3 (only remaining possible position in the block)
(60) If R7C9 contains the value 3, then R7C9 cannot contain the value 9 (the cell can contain only one value)
(61) If R9C9 contains the value 1 (53), then R9C9 cannot contain the value 9 (the cell can contain only one value)
(62) If R9C9 does not contain the value 9, R7C9 does not contain the value 9 (60), R2C9 does not contain the value 9 (52) and R3C9 does not contain the value 9 (47), then R8C9 must contain the value 9 (only remaining possible position in the column)

Chain 2:
If R8C9 must contain the value 9, then R8C9 cannot contain the value 9 (View 2):
(1) If R4C4 contains the value 7, then R4C4 cannot contain the value 1 (the cell can contain only one value)
(2) If R4C4 does not contain the value 1, then R6C4 must contain the value 1 (only remaining possible position in the block)
(3) If R6C4 contains the value 1, then R6C3 cannot contain the value 1 (the value can occur only once in the row)
(4) If R6C3 does not contain the value 1, then R7C3 must contain the value 1 (only remaining possible position in the column)
(5) If R7C3 contains the value 1, then R7C7 cannot contain the value 1 (the value can occur only once in the row)
(6) If R7C7 does not contain the value 1, then R3C7 must contain the value 1 (only remaining possible position in the column)
(7) If R3C7 contains the value 1, then R3C7 cannot contain the value 7 (the cell can contain only one value)
(8) If R7C3 contains the value 1 (4), then R7C3 cannot contain the value 7 (the cell can contain only one value)
(9) If R4C4 contains the value 7 (initial assumption), then R7C4 cannot contain the value 7 (the value can occur only once in the column)
(10) If R7C4 does not contain the value 7 and R7C3 does not contain the value 7 (8), then R7C5 must contain the value 7 (only remaining possible position in the row)
(11) If R7C5 contains the value 7, then R3C5 cannot contain the value 7 (the value can occur only once in the column)
(12) If R4C4 contains the value 7 (initial assumption), then R6C6 cannot contain the value 7 (the value can occur only once in the block)
(13) If R4C4 contains the value 7 (initial assumption), then R6C4 cannot contain the value 7 (the value can occur only once in the block)
(14) If R6C4 does not contain the value 7 and R6C6 does not contain the value 7 (12), then R6C9 must contain the value 7 (only remaining possible position in the row)
(15) If R6C9 contains the value 7, then R3C9 cannot contain the value 7 (the value can occur only once in the column)
(16) If R3C9 does not contain the value 7, R3C5 does not contain the value 7 (11) and R3C7 does not contain the value 7 (7), then R3C6 must contain the value 7 (only remaining possible position in the row)
(17) If R3C6 contains the value 7, then R3C6 cannot contain the value 3 (the cell can contain only one value)
(18) If R3C6 does not contain the value 3, then R1C4 must contain the value 3 (only remaining possible position in the block)
(19) If R1C4 contains the value 3, then R1C1 cannot contain the value 3 (the value can occur only once in the row)
(20) If R4C4 does not contain the value 1 (1), then R4C1 must contain the value 1 (only remaining possible position in the row)
(21) If R4C1 contains the value 1, then R4C1 cannot contain the value 3 (the cell can contain only one value)
(22) If R4C1 does not contain the value 3 and R1C1 does not contain the value 3 (19), then R8C1 must contain the value 3 (only remaining possible position in the column)
(23) If R8C1 contains the value 3, then R8C1 cannot contain the value 2 (the cell can contain only one value)
(24) If R4C1 contains the value 1 (20), then R4C1 cannot contain the value 2 (the cell can contain only one value)
(25) If R4C1 does not contain the value 2 and R8C1 does not contain the value 2 (23), then R5C1 must contain the value 2 (only remaining possible position in the column)
(26) If R5C1 contains the value 2, then R5C7 cannot contain the value 2 (the value can occur only once in the row)
(27) If R5C7 does not contain the value 2, then R9C8 cannot contain the value 2 (Pointing: Cells R4C8,R6C8: 2 of block in column)
(28) If R4C1 contains the value 1 (20), then R9C1 cannot contain the value 1 (the value can occur only once in the column)
(29) If R9C1 does not contain the value 1, then R9C1 must contain the value 7 (only remaining possible value in the cell)
(30) If R9C1 contains the value 7, then R9C5 cannot contain the value 7 (the value can occur only once in the row)
(31) If R9C5 does not contain the value 7, then R9C5 must contain the value 9 (only remaining possible value in the cell)
(32) If R9C5 contains the value 9, then R9C8 cannot contain the value 9 (the value can occur only once in the row)
(33) If R9C8 does not contain the value 9 and R9C8 does not contain the value 2 (27), then R9C8 must contain the value 8 (only remaining possible value in the cell)
(34) If R9C8 contains the value 8, then R4C8 cannot contain the value 8 (the value can occur only once in the column)
(35) If R4C4 contains the value 7 (initial assumption), then R4C4 cannot contain the value 8 (the cell can contain only one value)
(36) If R4C4 does not contain the value 8 and R4C8 does not contain the value 8 (34), then R4C5 must contain the value 8 (only remaining possible position in the row)
(37) If R4C5 contains the value 8, then R5C4 cannot contain the value 8 (the value can occur only once in the block)
(38) If R5C1 contains the value 2 (25), then R5C4 cannot contain the value 2 (the value can occur only once in the row)
(39) If R7C5 contains the value 7 (10), then R7C5 cannot contain the value 6 (the cell can contain only one value)
(40) If R7C5 does not contain the value 6, then R5C4 cannot contain the value 6 (Pointing: Cells R7C4,R8C4: 6 of block in column)
(41) If R5C4 does not contain the value 6, R5C4 does not contain the value 2 (38) and R5C4 does not contain the value 8 (37), then R5C4 must contain the value 9 (only remaining possible value in the cell)
(42) If R5C4 contains the value 9, then R5C3 cannot contain the value 9 (the value can occur only once in the row)
(43) If R4C1 contains the value 1 (20), then R4C1 cannot contain the value 9 (the cell can contain only one value)
(44) If R5C1 contains the value 2 (25), then R5C1 cannot contain the value 9 (the cell can contain only one value)
(45) If R8C1 contains the value 3 (22), then R8C1 cannot contain the value 9 (the cell can contain only one value)
(46) If R8C1 does not contain the value 9, R5C1 does not contain the value 9 (44) and R4C1 does not contain the value 9 (43), then R1C3 cannot contain the value 9 (Claiming: Cells R1C1,R2C1: 9 of column in block)
(47) If R1C4 contains the value 3 (18), then R1C4 cannot contain the value 9 (the cell can contain only one value)
(48) If R9C5 contains the value 9 (31), then R1C5 cannot contain the value 9 (the value can occur only once in the column)
(49) If R9C5 contains the value 9 (31), then R3C5 cannot contain the value 9 (the value can occur only once in the column)
(50) If R3C6 contains the value 7 (16), then R3C6 cannot contain the value 9 (the cell can contain only one value)
(51) If R3C6 does not contain the value 9, R3C5 does not contain the value 9 (49), R1C5 does not contain the value 9 (48) and R1C4 does not contain the value 9 (47), then R2C3 cannot contain the value 9 (Pointing: Cells R2C4,R2C6: 9 of block in row)
(52) If R6C3 does not contain the value 1 (3), then R6C3 must contain the value 3 (only remaining possible value in the cell)
(53) If R6C3 contains the value 3, then R3C3 cannot contain the value 3 (the value can occur only once in the column)
(54) If R3C3 does not contain the value 3 and R3C6 does not contain the value 3 (17), then R3C2 must contain the value 3 (only remaining possible position in the row)
(55) If R3C2 contains the value 3, then R3C2 cannot contain the value 2 (the cell can contain only one value)
(56) If R3C2 does not contain the value 2, then R3C3 must contain the value 2 (only remaining possible position in the block)
(57) If R3C3 contains the value 2, then R3C3 cannot contain the value 9 (the cell can contain only one value)
(58) If R3C3 does not contain the value 9, R2C3 does not contain the value 9 (51), R1C3 does not contain the value 9 (46) and R5C3 does not contain the value 9 (42), then R8C3 must contain the value 9 (only remaining possible position in the column)
(59) If R8C3 contains the value 9, then R8C9 cannot contain the value 9 (the value can occur only once in the row)

[daj95376]

ronk,

Here's what I get as the next four moves if I have Forcing Chains/Nets enabled.

Code: Select all

r7c5    <> 7 (3) [r7c5]=7 => [r7]=INVALID *
r4c4    <> 7     Forcing Chain/Net on [r6c3]
r3c6    <> 7 (4) [r3c6]=7 => [b2]=INVALID    (hidden,naked) = (12,18)
r4c4    <> 8 (3) [r4c4]=8 => [r5c4]=EMPTY    (hidden,naked) = (12,31)


Here's what I get if I have Forcing Chains/Nets disabled. You'll notice that the [r4c4]<>7 is now a pussycat.

Code: Select all

r7c5    <> 7 (3) [r7c5]=7 => [r7]=INVALID *
r3c6    <> 7 (4) [r3c6]=7 => [b2]=INVALID    (hidden,naked) = (12,18)
r4c4    <> 7 (4) [r4c4]=7 => [b8]=INVALID    (hidden,naked) = ( 1, 4)
r4c4    <> 8 (3) [r4c4]=8 => [r5c4]=EMPTY    (hidden,naked) = (12,31)


[Edit:] Just read your reply where other moves are also rated 10.0.

[ravel]

Today i started to scan Ocean's new list. What i already can say is that we have a new leader. Not very surprising the first (10.0 rated) puzzle needed more steps than Ocean's BB, namely 17, though i tried it with 5 versions of the puzzle, all both forward and backward. The 9.9 rated puzzles needed 8 and 9 steps. I suppose it will take me 2 more days for the whole list (i need the PC for other things also).


Maria,

please note the basic difference between the Explainer rating and my step counts:
While (as r.e.s. said) the Explainer only rates the hardest step, on the contrary i dont care about this, but only count the number of eliminations my program needs.
E.g. we had a 9.5 rated puzzle, which only needed 3 steps, so it did not qualify for the list. Or you can see that a 9.4 rated puzzle is number 2 in my current list.

I am happy that you are solving the puzzles manually and can judge the ratings from this side. When i looked at the length of your solutions, the rating seemed to be ok in the main. When you say, a puzzle is harder than another, because you needed more contradictions, this is also a matter of taste. I would prefer a contradiction to a forcing chain, if it is shorter. I also suppose that a slightly change of your strategy at the beginning could lead you to a much harder or easier solution. No one can see the easiest way in advance.

Sudoku Explainer's next move is r4c4<>7. Can anyone find an alternate move?

[Edit: typo 6, not 5]
After 7 eliminations (all done in the grid) my program eliminated 6 from r6c4 (it did not use r4c4<>7 in the 17 step solution).

[ronk]

My solver performs a complex [r7c5]<>7 elimination before [r4c4]<>7. But it still performs the second elimination.

I should have posted that Explainer chooses one of four possible exclusions it finds. It rates each exclusion as a 10.0 ... r4c4<>7, r7c5<>7, r3c6<>7, and r4c4<>8.

[maria45]

hm, a bit late, it seems, but I eliminated the r7c5=7 manually, too. But that was no difficult step, rather straight:

g5=7, (k1=7, g3=1, d1=1, f4=1, k9=1, c7=1, f3=3, f9=7, d7=3, g9=3, c6=7, d4=7, c2=3, h1=3, k6=3, a4=3, k5=9, e1=2, f2=6, c3=2, gh4=26, df8=2, k8=8, k2=2, d5=8, c5=6, a5=4, b6=9, e4=9, e3=5, a2=5, b9=5, b7=4, e9=4, h2=4, h3=8, box1!=8 contradiction >) g5!=7

[ronk]

but I eliminated the r7c5=7 manually, too

Before e9=4, don't you need c8=9, a8=6, and g8=4?

And when you have naked pair steps like "gh4=26, df8=2", I assume you make exclusions without specific assignments. Is that correct?

Nice job!

[Eioru]

I find this
.....4..7.9..8..2.6..3.......4.....8.5..7..9.1.....6..8....6.......2..5...19..3..
.....9..6.3..2..4.7..8.......3.....5.6..1..2.1.....7..2....5.......6..3...92..8..

[r.e.s.]

I should have posted that Explainer chooses one of four possible exclusions it finds. It rates each exclusion as a 10.0 ... r4c4<>7, r7c5<>7, r3c6<>7, and r4c4<>8.

Thanks for mentioning that. I've simply been stepping through the "default" solution path without trying to display the alternative moves available at each stage along the way.

My earlier question about individual moves with ER>10 is answered by just displaying more-and-more-difficult alternative moves at a given stage (using "Get Next Hint" repeatedly) -- in the present puzzle, there are many stages (e.g. even the very first move) where 10.5-rated moves are among the displayable alternatives.