The New Sudoku Players' Forum

by **tarek** » Thu Jul 23, 2020 10:59 am

Code: Select all: +-------+-------+-------+ | . . 3 | . 4 . | 2 5 . | | 8 . . | . . . | 1 . 4 | | . . . | . . . | . 9 8 | +-------+-------+-------+ | 3 . . | 9 . . | . . . | | . . . | . . . | . . 6 | | 2 8 1 | . . 6 | . . . | +-------+-------+-------+ | . 1 7 | 2 . . | . . 9 | | . . 9 | 3 . . | . . . | | . . . | 5 . 4 | . 2 . | +-------+-------+-------+ ..3.4.25.8.....1.4.......983..9.............6281..6....172....9..93........5.4.2.

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by **yzfwsf** » Thu Jul 23, 2020 11:35 am

Code: Select all: .-------------.---------------.--------------. | 1 6 3 | 8 4 9 | 2 5 7 | | 8 9 25 | 67 237 235 | 1 36 4 | | 7 45 245 | a16 123 235 | 3-6 9 8 | :-------------+---------------+--------------: | 3 457 6 | 9 8 17 | 45 147 2 | | 9 457 45 | b147 23 23 | 458 c1478 6 | | 2 8 1 | 47 5 6 | 9 47 3 | :-------------+---------------+--------------: | 5 1 7 | 2 6 8 | 34 34 9 | | 4 2 9 | 3 17 17 | e68 d68 5 | | 6 3 8 | 5 9 4 | 7 2 1 | '-------------'---------------'--------------'

(6=1)r3c4-r5c4=(1-8)r5c8=(8-6)r8c8=6r8c7 =>-6r3c7;stte

by **SpAce** » Thu Jul 23, 2020 12:56 pm

Code: Select all: A B C D E F G H I .-------------.----------------.-----------------. a | 1 6 3 | 8 4 9 | 2 5 7 | b | 8 9 25 | 67 237 235 | 1 c36 4 | c | 7 45 245 | a16 123 235 | b36 9 8 | :-------------+----------------+-----------------: d | 3 457 6 | 9 8 17 | 45 147 2 | e | 9 457 45 | a147 23 23 | 458 d478-1 6 | f | 2 8 1 | 47 5 6 | 9 47 3 | :-------------+----------------+-----------------: g | 5 1 7 | 2 6 8 | 34 34 9 | h | 4 2 9 | 3 17 17 | 68 d68 5 | i | 6 3 8 | 5 9 4 | 7 2 1 | '-------------'----------------'-----------------'

(16)ecD = cG - bH = (68)heH => -1eH; stte

(16)r53c4 = r3c7 - r2c8 = (68)r85c8 => -1 r5c8; stte

uncompressed aIrZ + rYcX: Show

by **Ajò Dimonios** » Thu Jul 23, 2020 2:16 pm

Code: Select all: +-----------+-------------+------------+ | 1 6 3 | 8 4 9 | 2 5 7 | | 8 9 25 | 67 237 235 | 1 36 4 | | 7 45 245 | 16 123 235 | 36 9 8 | +-----------+-------------+------------+ | 3 457 6 | 9 8 17 | 45 147 2 | | 9 457 45 | 147 23 23 | 458 1478 6 | | 2 8 1 | 47 5 6 | 9 47 3 | +-----------+-------------+------------+ | 5 1 7 | 2 6 8 | 34 34 9 | | 4 2 9 | 3 17 17 | 68 68 5 | | 6 3 8 | 5 9 4 | 7 2 1 | +-----------+-------------+------------+

7r8c5=7r2c5-(7=6) r2c4-6r2c8=(6-8)r8c8=(8-1)r5c8=1r5c4-1r3c4=1r3c5-(1=7)r8c5=>+7r8c5=>stte

by **SpAce** » Thu Jul 23, 2020 2:54 pm

Just to showcase some extra capabilities of the aIrZ-coordinates...

My previous solution in the nc-space:

Code: Select all: A B C D E F G H I .---------------.----------------.-----------------. 1 | a g f | Ace ch dh | b d-e i | 2 | f h bc | g bce bce | c b d | 3 | d i a | h bce bce | cg bg f | 4 | h cde ce | ef a i | deg defg b | 5 | g cde bce | i f bc | de a h | 6 | i a d | Abc g f | ch Bbh e | 7 | c de g | bef bh dh | i def a | 8 | b f i | a d g | eh Beh c | 9 | e b h | d i a | f c g | '---------------.----------------.-----------------'

(e=cb)16D - (bh=e)68H => -e1H; stte

That might be the shortest solution we'll see today. The same as a simple xy-chain:

(e=c)1D - (c=b)6D - (b=h)6H - (h=e)8H => -e1H; stte

It's not quite so nice in the rn-space:

Code: Select all: 1 2 3 4 5 6 7 8 9 .-------------------------------------------------. a | A G C E H B I D F | b | G CEF EFH I CF DH DE A B | c | bDE CEF EFG BC BCF cDG A I H | :-------------------------------------------------: d | FH I A BGH BG C BFH E D | e | aD-H EF EF BCDGH BCG I BDH fGH A | f | C A I DH E F DH B G | :-------------------------------------------------: g | B D GH GH A E C F I | h | EF B D A I dGH EF eGH C | i | I H B F D A G C E | '-------------------------------------------------'

(D)e1 = c1 - (D=G)c6 - h6 = h8 - (G=H)e8 => -He1; stte

...or a bit compressed:

(D)e1 = (DG)c16 - h6 = (G,H)he8 => -He1; stte

--

The point is that the aIrZ-system works very smoothly and unambiguously in any solving space (including various box-spaces; not shown) because each coordinate (n, r, c, b, p) has a different set of symbols. Of course very few people ever solve in anything other than the rc-space, but still. (It's actually quite fun and educating every once in a while.)

by **Ngisa** » Thu Jul 23, 2020 4:38 pm

Code: Select all: +-----------------+-------------------+------------------+ | 1 6 3 | 8 4 9 | 2 5 7 | | 8 9 25 |e67 237 235 | 1 d36 4 | | 7 45 245 | 16 123 235 | 36 9 8 | +-----------------+-------------------+------------------+ | 3 457 6 | 9 8 g7-1 | 45 a147 2 | | 9 457 45 |f147 23 23 | 458 b1478 6 | | 2 8 1 |f47 5 6 | 9 47 3 | +-----------------+-------------------+------------------+ | 5 1 7 | 2 6 8 | 34 34 9 | | 4 2 9 | 3 17 17 | 68 c68 5 | | 6 3 8 | 5 9 4 | 7 2 1 | +-----------------+-------------------+------------------+

(1)r4c8 = (1-8)r5c8 = (8-6)r8c8 = r2c8 - (6=7)r2c4 - r56c4 = (7)r4c6 => - 1r4c6; stte

Clement

by **SteveG48** » Thu Jul 23, 2020 5:00 pm

Code: Select all: *-----------------------------------------------------------* | 1 6 3 | 8 4 9 | 2 5 7 | | 8 9 25 | 67 237 235 | 1 36 4 | | 7 45 245 |c16 123 235 |d36 9 8 | *-------------------+-------------------+-------------------| | 3 457 6 | 9 8 b17 | 5-4 a147 2 | | 9 457 45 |c147 23 23 | 58-4 1478 6 | | 2 8 1 |c47 5 6 | 9 a47 3 | *-------------------+-------------------+-------------------| | 5 1 7 | 2 6 8 |d34 3-4 9 | | 4 2 9 | 3 17 17 | 68 68 5 | | 6 3 8 | 5 9 4 | 7 2 1 | *-----------------------------------------------------------*

(4=71)r46c8 - (1=7)r4c6 - (7=146)r356c4 - (6=34)r37c7 => -4 r45c7,r7c8 ; stte

(4=71)dfH - (1=7)dF - (7=146)cefD - (6=34)cgG => -4 deG,gH ; stte

The proposed coordinate system clearly saves a bit of space (no pun intended). My first problem with it, naturally, is figuring out which letters to use. Familiarity might
help there. The second problem is that I sometime have trouble distinguishing between i and I in the forum default font.

by **Cenoman** » Thu Jul 23, 2020 6:56 pm

Code: Select all: +-------------------+--------------------+--------------------+ | 1 6 3 | 8 4 9 | 2 5 7 | | 8 9 25 | z67 237 235 | 1 y36 4 | | 7 45 245 | 16 123 235 | 36 9 8 | +-------------------+--------------------+--------------------+ | 3 wA457* 6 | 9 8 17 |wB45 xa147* 2 | | 9 v457* 45 |za147* 23 23 | C458 C478-1 6 | | 2 8 1 | z47* 5 6 | 9 47* 3 | +-------------------+--------------------+--------------------+ | 5 1 7 | 2 6 8 | 34 y34 9 | | 4 2 9 | 3 17 17 | 68 68 5 | | 6 3 8 | 5 9 4 | 7 2 1 | +-------------------+--------------------+--------------------+

DP(47)r456c248 using internals
(1)r4c8,r5c4
(5)r4c2 - r4c7 = (58)r5c78
(5-7)r5c2 = (7-54)r4c27 = r4c8 - (4=36)r27c8 - (6=471)r256c4
=> -1 r5c8; ste
Edit: corrected typo (Thanks SteveC !)

by **SpAce** » Fri Jul 24, 2020 6:53 am

Hi Steve,

SteveG48 wrote:(4=71)dfH - (1=7)dF - (7=146)cefD - (6=34)cgG => -4 deG,gH ; stte

Thanks for trying it out!

The proposed coordinate system clearly saves a bit of space.

Yes, and the longer the chain the more it saves. In some cases the savings are also slightly larger if (bi)local links are favored over (bi)value links. For example, your ALS-chain above saves 16%, but if it's written with mixed links (all other things being equal), it saves 18% even though the starting chain is already shorter. The absolute saving is the same 12 characters:

Code: Select all: 77: (4=71)r46c8 - (1=7)r4c6 - (7=146)r356c4 - (6=34)r37c7 => -4 r45c7,r7c8 ; stte 65: (4=71)dfH - (1=7)dF - (7=146)cefD - (6=34)cgG => -4 deG,gH ; stte 68: (4=71)r46c8 - r4c6 = (16)r35c4 - (6=34)r37c7 => -4 r45c7,r7c8 ; stte 56: (4=71)dfH - dF = (16)ceD - (6=34)cgG => -4 deG,gH ; stte

(no pun intended)

Well, saving 'space' is trivial compared to saving 'SpAce'. Some souls are beyond redemption

My first problem with it, naturally, is figuring out which letters to use. Familiarity might help there.

There's a definite learning curve, but in my short experience it's not overwhelming. It takes a bit of practice but it's already starting to feel natural for me. However, before I get too comfy with it, I guess the choice of the letter sets would need to be reconsidered:

The second problem is that I sometime have trouble distinguishing between i and I in the forum default font.

Good of you to mention that. I haven't noticed that particular problem myself, but the 'I' is definitely a bit of a problem child with the forum font -- unless put in a CODE-block. That's why some systems have replaced it with 'j/J' or 'k/K'. I didn't go that route (not yet at least) because I wanted to keep things easy to remember. That's why I simply chose the first 9 and the last 9 letters in the alphabet, even though both sets have some issues.

Another reason was that if I really wanted to maximize readability, I don't think dropping the 'I' would be enough. For example, I think 'B' is an even bigger problem if next to an '8'. Mostly my system avoids those problems because digits aren't normally placed next to uppercase letters, but sometimes (like in the nc-space, or with alien fishes) it's unavoidable. Thus, it would be best to avoid all ambiguously shaped letters that can be confused with digits or other letters. For example, in hand-writing 'g' and '9' look very similar, and so do 'G' and '6', so that's another problem letter. Also, 'u' and 'v' might look a bit similar at first glance, and even 'A' and '4', though I guess they're minor problems. I don't particularly like 'w/W' either, but it's for different reasons. For one, it's a wide character in a non-fixed font, and even more importantly, it's a three-syllable word when pronounced, which is annoying when reading coordinates even in your head.

So, I'm definitely open for suggestions, if someone has better ideas for a set (or rather, two sets) of letters to use. For your problem with the 'i' vs 'I' even the normal NrC-ordering doesn't help, because they're routinely placed next to each other. The simplest route would be to replace 'i/I' with 'j/J' or 'k/K', but a more comprehensive readability-optimization could get quite complicated and difficult to remember. Since readability is a major goal for me, I'm of course open for all possibilities, as long as they can be relatively easily remembered (for example, if the letters form a nice mnemonic then even strict alphabetical order isn't a must).

PS. Cenoman, I'm also very interested in your opinion, as you probably have the most experience with different coordinate systems. Have you seen any before that use letters for both rows and columns? Personally I think it's far superior to the common ones that use letters only for one coordinate, because it allows unambiguous addressing of any coordinate without further qualifiers and leaves the digits for the n-coordinate only. Also, have you seen any that can address box-coordinates the same way? While that complicates things by having to remember 18 letters instead of 9, I think it's quite essential for box-based subsets and fishes. (Another possibility I considered was an escape mechanism that would allow to use the same letters for boxes and positions as for rows and columns, but it would have other complications.)

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