## Two questions on one puzzle

All about puzzles in newspapers, magazines, and books

### Two questions on one puzzle

On this puzzle, I have two questions.

Code: Select all
`Frank Longo Second Degree Black Belt Sudoku #9 - Sterling *-----------* |23.|48.|9..| |..5|312|.7.| |...|9.5|432| |---+---+---| |...|.2.|.67| |.62|.3.|.89| |17.|.9.|...| |---+---+---| |729|8.3|...| |3..|.49|7..| |..4|..1|.93| *-----------* *-----------------------------------------------------------* | 2     3     67    | 4     8     67    | 9     15    15    | | 49    49    5     | 3     1     2     | 68    7     68    | | 68    18    167   | 9     67    5     | 4     3     2     | |-------------------+-------------------+-------------------| | 459   49    38    | 15    2     48    | 135   6     7     | | 45    6     2     | 157   3     47    | 15    8     9     | | 1     7     38    | 56    9     68    | 235   245   45    | |-------------------+-------------------+-------------------| | 7     2     9     | 8     56    3     | 56    14    14    | | 3     158   16    | 26    4     9     | 7     25    68    | | 68    58    4     | 267   567   1     | 2568  9     3     | *-----------------------------------------------------------*`

1. According to Simple Sudoku, I should be able to eliminate the 6 pencil mark in R9C4 using "multiple colors". I can't figure out how that is done. Is it the same as trying out a chain of doubles and coming up with an inconsistency? I would appreciate any help in a) understanding this particular case, and b) helping me to see how an ordinary mortal can find this type of solution in general.

2. In R2C1&2 and R4C1&2 we have 4s & 9s with a five in R4C1. If R4C1 is not a 5 then it could be either a 4 or 9, and there might be two solutions to the puzzle. Is that a legitimate clue to the puzzle, or should there be some other way of placing the 5 there?

Thanks,
John Fistere
JFistere

Posts: 27
Joined: 09 December 2005

The 5 has to go in R4C1 due to unique rectangle. Anything else would lead to an invalid puzzle. I don't understand multiple colouring though; good luck.
Hud

Posts: 570
Joined: 29 October 2005

Simple Sudoku does not support Unique Rectangles, and so it tries to proceed using the techniques it does support. In this case, SS uses Mulit-Colors to eliminate the <6> in [r9c4]. Unfortunately for SS, this is only a stalling process because it gets trapped a little later where it can't proceed.

Your spotting the Unique Rectangle Type 1 in <49> was good. It allows you to eliminate <49> from [r4c1] and this leaves only the <5> as the value for this cell. The puzzle cracks at this point and is solvable with basic techniques.

There are numerous threads in this forum and in the Programmers Forum on how Multi-Colors works. I don't think you're going to get anyone here to write a new explanation for you. Time to do some research!!! I suggest you start with the Help facility in SS.
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

Thanks Hud and daj,
I did check the Multiple Colors Help in SS, but I couldn't figure out the particular Multiple Colors of the puzzle.

I think I understand tracking doubles to try a number to see if a contradiction develops (although I haven't used it successfully yet). Multiple Colors seems similar, and I am wondering if it is another way of implementing the same technique, or if it is actually a different method.

I take your point on Multiple Colors in general, and I will search for some discussions of the subject.

John Fistere
JFistere

Posts: 27
Joined: 09 December 2005

Code: Select all
` *-----------------------------------------------------------*  | 2     3    A67    | 4     8    a67    | 9     15    15    |  | 49    49    5     | 3     1     2     | 68    7     68    |  |B68    18    167   | 9     67    5     | 4     3     2     |  |-------------------+-------------------+-------------------|  | 459   49    38    | 15    2     48    | 135   6     7     |  | 45    6     2     | 157   3     47    | 15    8     9     |  | 1     7     38    |a56    9    A68    | 235   245   45    |  |-------------------+-------------------+-------------------|  | 7     2     9     | 8     56    3     | 56    14    14    |  | 3     158   16    | 26    4     9     | 7     25    68    |  |b68    58    4     |-267   567   1     | 2568  9     3     |  *-----------------------------------------------------------* `

The "multiple colors" move works like this:
multiple colors wrote:If r9c4=6 => r6c4<>6 (a) => r6c6=6 (A) => r1c6<>6 (a) => r1c3=6 (A)
If r9c4=6 => r9c1<>6 (b) => r3c1=6 (B)
And we have two 6s in box 1!
Therefore r9c4<>6

Some would call this technique "turbot chain" - a more complicated instance of "turbot fish"...
This is another pattern/strong links based technique...
udosuk

Posts: 2698
Joined: 17 July 2005