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Steve R · Posted: Sat Aug 04, 2007 2:57 pm Post subject: Chapeau!

Congratulations to ravel on discovering the first minimal puzzle with 38 clues, which he published on 17 July:

Asellus · Posted: Sun Aug 05, 2007 12:08 am Post subject:

Nice puzzle.

I don't believe I found the "plain sailing" route. It took me 8 steps. All fairly well-known hereabouts... no chains, nothing uniqueness-based, no exotic coloring or the like.

Marty R. · Posted: Sun Aug 05, 2007 12:50 am Post subject:

Asellus · Posted: Sun Aug 05, 2007 1:27 am Post subject:

Marty's question sent me looking and I found these:

http://www.sudopedia.org/wiki/Minimal

http://www.sudopedia.org/wiki/Locally_minimal

http://www.sudopedia.org/wiki/Symmetrically_minimal

I have a question:

Is 38 the largest number of givens that has ever been found for a minimal puzzle, or are there minimal puzzles of, say, 39 or 40 givens but none of 38 had been found before?

Steve R · Posted: Sun Aug 05, 2007 1:30 am Post subject:

Asellus

Yes, it looks as though we might have gone different ways. I don’t know how many steps I took but it was certainly eight or thereabouts. I’m glad you enjoyed it. So did I though I wouldn’t want one like that every day.

Marty

A puzzle is minimal if it has a unique solution while the removal of any clue results in a puzzle with more than one solution. Evidently there is an upper limit to the number of clues which a minimal may have. It is far from certain that we shall ever find out what it is. To date work has concentrated on using computers to discover heavily clued puzzles.

I believe ravel suspects there will be a thirty-niner and is continuing the search.

Steve

PS (Added after Asellus's most recent post)

38 is the highest yet found. In the other direction 40,000 odd minimal puzzles with 17 clues are known.

keith · Posted: Sun Aug 05, 2007 9:33 pm Post subject: I don't see it ...

After an X-wing and a W-wing:

Asellus · Posted: Sun Aug 05, 2007 9:48 pm Post subject:

Keith,

Look at R1349 and think big!

keith · Posted: Sun Aug 05, 2007 11:44 pm Post subject:

I still don't see it.

If it is a chain, I don't buy it.

Keith

Steve R · Posted: Mon Aug 06, 2007 1:52 am Post subject:

I didn't spot Asellus's fish. My next six steps were:

1 Eliminate 8 from r2c5 using the conjugates (r5c1, r5c5) and (r2c2, r6c2) with respect to 8.
2 Eliminate 9 from r3c7 and r3c8 using the w-wing pivoted on the conjugates (r1c6, {r3c5, r3c6}) with respect to 8 and the pincers (89) in r1c7 and r3c1
3 Eliminate 7 from r6c8 using the xy-wing for (19) pivoted on r5c8 with pincers r3c8 and r6c9
4 The only place for 7 in column 8 is r3c8
5 Eliminate 1 from r5c5 using the w-wing pivoted on the conjugates (r2c3, r5c3) with respect to 9 and the pincers (19) in r2c5 and r5c8
6 The only place for 1 in row 5 is r5c8

Singles follow. (At least I hope they do: I didn't quite have Keith's position. It was very close and I have bodged to fill the gap.)

Steve

Asellus · Posted: Mon Aug 06, 2007 2:29 am Post subject:

As Steve noted, I was hinting at the Finned Jellyfish on 9. It eliminates <9> from R2C7.

Next, I too eliminated <8> from R2C5, though I saw it as a Box 1 ER using the R5 pair rather than as Steve's "Kite" or "Color Wrap". (So many ways to see the same thing.)

After that...

XY Wing: Pivot R2C7 eliminates <9> from R1C6. 8, 5 and 4 are now determined in C5, <1>s simplify a bit, etc.

Color Wrap or Kite out of Box 7 eliminates <9> from R2C5.

Then, an XY Wing: Pivot R6C8 eliminates <9> from R7C9, finishing things off.