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nataraj · Posted: Tue Dec 18, 2007 7:46 am Post subject:

O.K., I'll chip first.

As Keith suggested, I tried a UR (69) in r89c25, which leaves r9c2 with {2,8}
This cell is the fin in a finned x-wing on "2". This is the pattern, the fin is marked @. xwing would be in in c29. Take out 2 from r7c1.

ravel · Joined: 21 Apr 2006 Posts: 536

Really hard, cant see something nice.

storm_norm · Joined: 18 Oct 2007 Posts: 1741

this has a 13,633 rating on the sudokusolver.co.uk solver

the highest any of the VH's get is 2,000-3,000

and just to give a base comparison, the white belt sudoku book puzzles have a 20-100 rating

the hardest puzzles known to date average 100,000-300,000

and oh by the way, this puzzle was completed by the solver in 13 seconds using its guessing routine.

the "golden nugget" referenced in some other threads as the toughest so far took the solver over 4 minutes to hack away brute force.

norm

keith · Posted: Tue Dec 18, 2007 10:12 pm Post subject:

I was playing with Sudoku Susser on this one. It has something called "Trebor's Tables".

For example, R1C5 is <15>.

If R1C5 is <5>, you can solve <5> and <7> in R3, then <1> in C9.

So, for all possible values of R1C5, R1C9 is not <1>.

Interesting, but I think it would take a human an infinite amount of time (and pencils and paper and erasers) to do this.

Asellus · Posted: Wed Dec 19, 2007 5:48 am Post subject:

ravel,

Your nice cycle chain should actually read:
(1)r1c5-(1)r1c8=(1)r9c8-(1=7)r8c9-(7)r3c9=(7-5)r3c7=(5)r3c4-(5=1)r1c5
(At first glance, it looked as if you'd written a discontinous loop.)

And, you missed some resulting eliminations: (7-5)r3c7 also becomes a conjugate link, and hence a bivalue. So, <6>, <8> and <9> are all eliminated from r3c7.

I haven't yet tried to determine whether this is of any help with the puzzle.

nataraj · Posted: Wed Dec 19, 2007 6:49 am Post subject:

For people with a visual mind like mine, here's the graphic representation of ravel's nice loop, together with the eliminations it makes. Haven't got time yet to continue but I am sure we'll get this one in a finite amount of time.

Together with ravel's second AIC, this is where we are:

nataraj · Posted: Wed Dec 19, 2007 7:22 am Post subject:

O.K., here's the Medusa color plot, starting from "1"

There is already one elimination we can make immediately:

r4c3<>7 (sees red 7 in r8c3 and green 5 in its own cell)

happy hunting ....

nataraj · Posted: Wed Dec 19, 2007 7:32 am Post subject:

Some more from Medusa:

the elimination of 7 from r4c3 gives a strong link on 7 in c3 -> color 7 in r6c3 green.

If RED is true, then in col 3, candididate 2 can go ONLY into cell r6c3. (reason:
- red 1 in r2c4 => r2c1=2 => r1c3<>2
- red 5 in r5c3 => r5c3<>2
- red 1 in r9c3 => r9c3<>2)

This allows elimination of 8 and 9 from r6c3. R6c3 is now bi-value and we can color 2 in r6c3 red.

or plain "code":

Asellus · Posted: Wed Dec 19, 2007 9:11 am Post subject:

While nataraj was doing that coloring, I was doing something similar but exploiting some Deadly Patterns (DPs). I hope I haven't made any logical lapses!

nataraj · Posted: Wed Dec 19, 2007 9:31 am Post subject:

Nice going, Asellus.
I went another way, but I,too arrived at r6c1=7. (Must go over my notes again to post here).
In the meantime, taking "the grid now", there are a few box/line eliminations that can be made:

Asellus · Posted: Wed Dec 19, 2007 9:58 am Post subject:

I caught that Box-Line thing and editted while you were working on it. (Aren't overlapping posts fun?)

I've made more progress. First, there is a Kite pivoting in Box 1 that removes <9> from r9c7. This leads to some more fancy coloring based on a DP:

Asellus · Posted: Wed Dec 19, 2007 10:03 am Post subject:

The <3> in r4c2 is toast, also, due to the R-B coloring. That helps a bit.

Asellus · Posted: Wed Dec 19, 2007 10:49 am Post subject:

Next, there was a {68} Type 4 UR in r46c16 (<6>s linked in c1) that removed <8> from r4c1. That gets things here:

ravel · Joined: 21 Apr 2006 Posts: 536

nataraj · Posted: Wed Dec 19, 2007 12:37 pm Post subject:

keith · Posted: Wed Dec 19, 2007 2:35 pm Post subject:

Asellus · Posted: Wed Dec 19, 2007 10:02 pm Post subject:

nataraj,

You're not seeing the Kite because you aren't considering strong links with a "grouped end." The "string" of the Kite in r2 is obvious. The other string is in c3: pincer end at r9c3 is strongly linked with the 2 <2>s grouped in Box 1, r13c3. Or...

(9)r9c7-(9)r2c7=(9)r2c1-(9)r13c3=(9)r9c3-(9)r9c7

ravel,

Nice DP work at the end! (I wish I had noticed that Type 6!) It is interesting how much of the solution to this puzzle depended upon various DPs. I guess that's not surprising since DPs induce links that are otherwise not at all evident.

Just so it's clear... the grid from which you last worked with those DPs is the grid that resulted after that involved coloring step utilizing the two DPs in the central tower (not the grid after your earlier AIC loop).

nataraj · Posted: Thu Dec 20, 2007 5:52 am Post subject:

[quote="Asellus"]nataraj,

You're not seeing the Kite because you aren't considering strong links with a "grouped end." The "string" of the Kite in r2 is obvious. The other string is in c3: pincer end at r9c3 is strongly linked with the 2 <2>s grouped in Box 1, r13c3. Or...

(9)r9c7-(9)r2c7=(9)r2c1-(9)r13c3=(9)r9c3-(9)r9c7

Thanks for the explanation, Asellus! Indeed, I did not look at that r13c3 group.

@ravel & Asellus: Congratulations!