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Marty R. · Posted: Mon Oct 06, 2008 3:41 pm Post subject: Hopelessly stuck

This is another Outlaw puzzle from Paul's Pages. I haven't made a single move, although a hidden UR will remove the 5 from r8c5. Most if the time Extended Medusa can bail me out, but not here.

storm_norm · Joined: 18 Oct 2007 Posts: 1741

marty, don't be too down about this one. according to sudocue this could involve

3 medusa traps
4 medusa bridges
4 medusa complexes

nataraj · Posted: Tue Oct 07, 2008 7:45 am Post subject:

Medusa will help when extended ...

Starting at r3c6, This is where Medusa takes us (red and green background).

Looking only at "red", we see
a) r7c6<>4 (because of r3c6=4)
b) r7c7=9 (because of r8c7=8, sl 9 in box 9), thus r7c6<>9

If r7c6 is neither 4 nor 9, it must be 1

c) r2c4=9 (because of r2c6=7, sl 9 in row 2), thus r9c4<>9

If r9c4<>9 it must be 1.

This is a Medusa wrap, it solves r3c6 and some more cells.

After that (and I did use that UR wsl Marty mentioned), a skyscraper (6) is enough to solve the puzzle.

daj95376 · Joined: 23 Aug 2008 Posts: 3854

ravel · Joined: 21 Apr 2006 Posts: 536

Nataraj said: This is a Medusa wrap, which means that this (red) branch cant be true. It would lead to both r7c6=1 (b) and r9c4=1 (c).
Therefore the red starting point r3c6=4 must be wrong and the greens are true.

PS:
Extended Medusa is also known as Red Green Transport (but the wrap - a contradiction in one branch, which you often will get - is not mentioned there).

This is probably the most effective technique to solve harder puzzles on paper, where the normal arsenal of techniques fails. Just try to find a good starting point (e.g. bivalue cells or conjugated numbers), where both branches easily can be extended.
Drawbacks: It is hard to describe the solution to others and if you are (un)lucky, one branch directly will solve the puzzle.

Marty R. · Posted: Tue Oct 07, 2008 3:51 pm Post subject:

Extended Medusa usually rescues me on difficult puzzles, but I tried it twice here without any success. Thanks for the responses.

nataraj · Posted: Tue Oct 07, 2008 7:12 pm Post subject:

Thanks for the clarification, ravel! Actually what I did was not Medusa per se and not Asellus' extension, but the "graded equivalence marks", or GEM for short. GEM can lead to eliminations (what in Medusa parlance is called "traps") or to a contradiction ("wrap"), or both. I rarely use Medusa/GEM - I've decided for myself that the method is all too dependent on the starting point -, but since Medusa was explicitly mentioned by Marty and storm_norm, I gave it a try.

The results (if there are any) can be described adaequately by AICs, although in many instances one needs grouped or even branched AICs and that does get very messy. therefore I rely mostly on the drawings like I did in this example, here, together with a few immediately obvious conclusions ("if x=a then y<>a then ..." seems to be the most understandable and simple type of explanation. Personally I've never felt comfortable with reasoning involving green and red, although it is extremely helpful to remember that in Medusa colored grids either all reds are true or all greens)
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edited to correct meaning of GEM = graded equivalence marks. The article on GEM is in sudopedia

Asellus · Posted: Tue Oct 07, 2008 8:52 pm Post subject:

daj95376 · Joined: 23 Aug 2008 Posts: 3854

Okay, I now understand that red represents a forcing net for [r3c6]=4 that leads to the contradiction [r7c6]=1 and [r9c4]=1.

It has several cells in common with this SIN:

Asellus · Posted: Wed Oct 08, 2008 7:23 am Post subject:

Having sort of started this "extended" Medusa thing on this board, I have come to avoid any "extensions" that are not obvious without markings (not that I'm saying the extensions above are not obvious... that is up to each person to decide) so as to avoid anything too elaborate that threatens to become forcing (or extended color markings that then have to be erased to continue). Instead, I prefer to opt for Medusa multi-coloring.

GEM is probably a more efficient approach to this puzzle. But, GEM is complex and not so easy to learn. Medusa multi-coloring is more straightforward than GEM, if not as powerful. In the case of this puzzle, it is only moderately efficient. An example of a grid template that can be used for pencil and paper Medusa multi-coloring is here.

I started in r4c7 with an "Aa" cluster, then added a "Bb" cluster with weak link bridge on the <7>s in c2 to give an "ab" strong pair.