Mystery Decompression Sudoku

For fans of Killer Sudoku, Samurai Sudoku and other variants

Mystery Decompression Sudoku

The following line represents a Sudoku which I also posted on my special page today. The digits are the given numbers and the letters A, B, C and D replace the empty cells. Each letter represents a decompression instruction like “insert 2 empty cells”. The letters have no specific order. That would be too easy. However, to help you on your way, I will give you a hint: The given numbers form a symmetrical pattern.
Code: Select all
`A9CA37BD4AC1AC1C28BC68A9BC7DC1BCA7A64BA23C6B5AC2BC83AC9`

Enjoy
Ruud
[edit: error fixed]
Last edited by Ruud on Mon Nov 13, 2006 8:10 am, edited 1 time in total.
Ruud

Posts: 664
Joined: 28 October 2005

Can we assume that each letter (A, B, C, D) represents a different number of cells to be inserted?

Bill Smythe
Smythe Dakota

Posts: 564
Joined: 11 February 2006

Smythe Dakota wrote:Can we assume that each letter (A, B, C, D) represents a different number of cells to be inserted?

No. One of the letters represents a different instruction.

Ruud
Ruud

Posts: 664
Joined: 28 October 2005

Ruud wrote:.... No. One of the letters represents a different instruction. ....

That's what I was beginning to suspect.

The string has 24 digits, 11 A's, 7 B's, 11 C's, and 2 D's. So if each letter represented a different number of blank cells, we would have:

11A + 7B + 11C + 2D <= 57

where here A means the number of blank cells represented by the letter A, etc. 57 is the total number of blank cells (81-24). Because there might be a missing "letter" at the end of the string, we have <= rather than =.

Of course, the above inequality cannot be solved using distinct, positive integers A, B, C, D (the smallest possible total is 62).

I then looked at the double letters (and one triple letter). I found:

BA
CA
DA
AC (four times)
BC (three times)
BD
BCA

B appears only as the first letter, never the second, in any pair. So it was my thought that B might stand for a carriage-return-linefeed, i.e. "go to the beginning of the next row". There are only six B's, rather than the expected eight (you wouldn't need one at the end of r9), perhaps because two rows have a digit in c9 (eliminating the need for a CR/LF in that row) or maybe because r9 might be entirely blank.

As for A, C, D, I notice there are no doubles (AA, CC, DD). So maybe something binary is going on here, like A=1, C=2, D=4. This would make it possible to represent any number of blanks from 1 through 7 without repeating any letter. One wouldn't need to represent 8 or 9, because a CR/LF would do the trick instead.

That's where I am right now. I still don't know why both AC and CA appear in the string, when the use of either of them consistently would suffice. Maybe, just like the concrete in "the dog that eats concrete", it was just thrown in to make it harder.

Or (more likely), maybe I'm just way off base with this whole CR/LF theory.

Bill Smythe
Smythe Dakota

Posts: 564
Joined: 11 February 2006

Bill,

your reasoning is impeccable. Seems like you almost found it.

Ruud
Ruud

Posts: 664
Joined: 28 October 2005

Re: Mystery Decompression Sudoku

Ruud wrote:The following line represents a Sudoku which I also posted on my special page today...
Code: Select all
`A9CA37BD4AC1AC1C28BC68A9BC7DA1BCA7A64BA23C6B5AC2BC83AC9`

By modifying one letter we can get an interesting puzzle solvable with xyz-wing, xy-wing, triplet, pairs, lc:
Code: Select all
`A9CA37BD4AC1AC1C28BC68A9BC7DC1BCA7A64BA23C6B5AC2BC83AC9 *-----------* |..9|...|37.| |...|.4.|..1| |...|1.2|8..| |---+---+---| |.68|..9|...| |.7.|...|.1.| |...|7..|64.| |---+---+---| |..2|3.6|...| |5..|.2.|...| |.83|...|9..| *-----------*`
Ocean

Posts: 442
Joined: 29 August 2005

ocean, that was a very polite way to say that you found an error in my string...

Thanks. I will correct the original post. (and my special page)

Ruud
Ruud

Posts: 664
Joined: 28 October 2005

Finlip

Posts: 49
Joined: 15 July 2005

Re: Mystery Decompression Sudoku

Ocean wrote:By modifying one letter we can get an interesting puzzle solvable with xyz-wing, xy-wing, triplet, pairs, lc:

Thanks Ocean for the great correction... Just like to comment that the xyz-wing is necessary (?) and the xy-wing is not... So, singles, pairs, triples, locked candidates plus 1 xyz-wing are all the weapons you need to crack this one...

Here is the answer/spoiler, which is essentially worked out by Bill Smythe (great work! ):

The code:
A9CA37BD4AC1AC1C28BC68A9BC7DC1BCA7A64BA23C6B5AC2BC83AC9

The 4 letters have the following instructions/replacements:
A=..
B=new line
C=.
D=....

Puzzle grid:
..9...37.
....4...1
...1.28..
.68..9...
.7.....1.
...7..64.
..23.6...
5...2....
.83...9..

Solution grid:
149568372
827943561
356172894
468219753
975634218
231785649
712396485
594827136
683451927

udosuk

Posts: 2698
Joined: 17 July 2005