My app has one top level that is hard. I regularly cheat because I get to a point where I have to guess between 2 options for 1 or 2 squares. But the program counts up to 3 'mistakes' as a perfect game.
I guess this designer is saying you have to work forward from one of several 'possible' solutions for a square for several moves before you discover whether you are right or wrong.
Anyway, cool.
I don't see what's so hard. There are 71 blank cells. That's only 5.8e+120 combinations. Just try them out.
There are 21 cells filled in, and I thought you could get down to 17 with it still being solvable to a unique solution. So 21 seems easier ...
I mostly do killer sudoku or kenken these days, because I am more of an arithmetician than Heebie.
(Don't anyone give away any answers yet, I have no time for the next 24 hours.)
I presume a move means filling in a number, which may or may not be correct because the square is underdetermined at that stage. Thinking ten moves ahead means filling in a number, figuring out the consequences of that, filling in another number, working out the consequences, etc for 10 moves, until you realise you've created a broken "solution" and you try a different number for your first move.
I think he's saying that you'll reach points where you can't just consider the current shape of the board, you'll have to think ahead. So in easier Sudoku, there's always a few spaces on the board where the answer is obvious and those answers lead you to other spaces where the answer is obvious and so on until the board is full. You're never actually guessing. But in the really advanced Sudokus, sometimes you hit a point where there is no reason to know exactly how any still empty square should be filled. That's when most people guess, and see how it plays out. Often you figure out really quickly -- within a couple more squares -- whether your guess was right or not. He's suggesting that at those "guess" moments, it might take ten squares or more to find out whether you guessed correctly. Also, I suspect he thinks that instead of guessing and playing it out to see whether you guessed correctly, you should figure out the entire if/then logic string in your head.
On my app, the Expert level always reaches that guess moment eventually. I find it tedious. I'd rather try to break five minutes on the Hard level where there's always a logical answer to at least one square then have to do all that advance planning.
4: That's what I'd assume too, except it's not how the super-difficult strategies work. The super-difficult strategies all involve contemplating possibilities in a large number of squares and drawing a deduction which allows you to reduce a possibility somewhere.
And then what you're describing does happen, and very simplistically, at times: if you have a long chain of squares with two possibilities, where chain-adjacent squares share a possible entry, it's very easy to say "Suppose this one is an X" and watch that trickle down throughout the chain. So it's not really the hallmark of a difficult deduction.
On the app I do, under "hints" you can fill in all the possibilities. IMO, filling in possibilities is just super tedious, and the game starts once you've got them laid out, so I always use this hint. So you can start at a level where there isn't anything obvious.
Wow, I always feel a little like I'm being lazy when I write the possibilities into the box to narrow them down. Having the possibilities as a given -- it must feel like a totally different game. Nice!
It's a completely different game! The other thing this app has is explanations of some of the more difficult moves. I've come to believe that the game doesn't start until the possibilities are all filled in. That the game is how to whittle down possibilities, one at a time.
under "hints" you can fill in all the possibilities
I'm trying to understand what this means. What level of possibilities does it eliminate? Any direct in-a-line numbers that it can rule out? Then you are left with two or more way inferences?
My somewhat human-like solver has to "guess" (apply lookahead) at least six times, which is a lot (one or two guesses are typical for the hardest of newspaper puzzles), and three of those guesses are in the first four deductions in the run below. So I'm convinced that it's a very hard puzzle. No doubt Inkala has a formal measure of "hardness" but he doesn't seem to have published his work anywhere so I don't know what it is.
$ ./testsudoku < worlds-hardest
Solving puzzle:
8 . . | . . . | . . .
. . 3 | 6 . . | . . .
. 7 . | . 9 . | 2 . .
---------------------
. 5 . | . . 7 | . . .
. . . | . 4 5 | 7 . .
. . . | 1 . . | . 3 .
---------------------
. . 1 | . . . | . 6 8
. . 8 | 5 . . | . 1 .
. 9 . | . . . | 4 . .
Solution:
8 1 2 | 7 5 3 | 6 4 9
9 4 3 | 6 8 2 | 1 7 5
6 7 5 | 4 9 1 | 2 8 3
---------------------
1 5 4 | 2 3 7 | 8 9 6
3 6 9 | 8 4 5 | 7 2 1
2 8 7 | 1 6 9 | 5 3 4
---------------------
5 2 1 | 9 7 4 | 3 6 8
4 3 8 | 5 2 6 | 9 1 7
7 9 6 | 3 1 8 | 4 5 2
Grading puzzle:
Guessing 9 at 6,7 (1 possible guess with 2 options).
Guessing 3 at 6,6 (1 possible guess with 2 options).
Guessing 2 at 1,6 (3 possible guesses with 2 options).
Guessing 7 at 8,7 (8 possible guesses with 2 options).
Guessing 9 at 0,1 (10 possible guesses with 2 options).
Guessing 6 at 2,8 (9 possible guesses with 2 options).
Hardest move was MASTER.
. 34e 10e | 05e 29e 30e | 33e 22e 26e
09m 23e . | . 54e 55e | 36e 08e 28e
35e . 06x | 21e . 39e | . 38e 27e
---------------------------------------
45e . 15e | 58e 43e . | 37e 59e 48e
44e 51e 14n | 56e . . | . 57e 47e
46e 50e 13e | . 49e 18x | 17e . 16e
---------------------------------------
02x 03m . | 19e 04n 20e | 01m . .
24e 25e . | . 53e 52e | 00m . 07m
12e . 11m | 41e 40e 42e | . 31e 32e
What level of possibilities does it eliminate? Any direct in-a-line numbers that it can rule out? Then you are left with two or more way inferences?
Given a square, this hint eliminates anything in the square's row, column, or group of 6. Given a sufficiently easy puzzle, there might only be one possibility revealed.
Ok, Gareth: I'm going to go get one of the toughest puzzles from my app. Can you plug it in your magic solver for comparison?
* 8 * | * * * | * * *
7 * * | 1 * * | * * *
5 1 6 | * * 4 | * 7 2
-----------------------
* 5 8| * * 6 | * 3 *
3 * * | * * * | * * 1
* 6 * | 2 * * | 4 5 *
-----------------------
4 3 * | 5 * * | 7 8 9
* * * | * * 7 | * * 4
* * * | * * * | * 6 *
I could actually make some progress on this one, and then when I needed a hint it was something called a 3D Medusa Coloring, which I have no fucking clue what that means.
OK, for your puzzle my solver makes 12 deductions and then it has to guess once, which is typical behaviour when it's given a hard newspaper puzzle. (My solver does not know about "3d medusa colouring", but there's a clear explanation here.)
$ ./testsudoku < heebies-puzzle
Solving puzzle:
. 8 . | . . . | . . .
7 . . | 1 . . | . . .
5 1 6 | . . 4 | . 7 2
---------------------
. 5 8 | . . 6 | . 3 .
3 . . | . . . | . . 1
. 6 . | 2 . . | 4 5 .
---------------------
4 3 . | 5 . . | 7 8 9
. . . | . . 7 | . . 4
. . . | . . . | . 6 .
Solution:
9 8 2 | 6 7 3 | 1 4 5
7 4 3 | 1 2 5 | 8 9 6
5 1 6 | 8 9 4 | 3 7 2
---------------------
2 5 8 | 4 1 6 | 9 3 7
3 9 4 | 7 5 8 | 6 2 1
1 6 7 | 2 3 9 | 4 5 8
---------------------
4 3 1 | 5 6 2 | 7 8 9
6 2 9 | 3 8 7 | 5 1 4
8 7 5 | 9 4 1 | 2 6 3
Grading puzzle:
Guessing 2 at 1,7 (14 possible guesses with 2 options).
Hardest move was MASTER.
21e . 25e | 02e 05e 35h | 32e 31e 36e
. 27e 26e | . 16e 44e | 43e 34e 04e
. . . | 51e 52e . | 42e . .
---------------------------------------
19e . . | 23e 22e . | 18e . 08e
. 28e 29e | 09e 46e 45e | 03e 17e .
20e . 10e | . 39e 40e | . . 07e
---------------------------------------
. . 15e | . 01e 14e | . . .
00e 12m 49e | 41e 50e . | 38e 33e .
06e 11e 47e | 48e 30e 24e | 13e . 37e
So the puzzle in the OP is substantially harder than what my app maxes out at. Although the hardest move sounds about equivalent.
Which was actually my experience of working on the puzzle in 14 - it seemed weirdly easy for the "nightmare" level, except for one crazy-difficult move.