I'd like to open a discussion on the manipulative sudoku of part 2 of WSC 2011.
Here are the rules:
"This is a manipulative Sudoku puzzle
where small pieces with pictures are to
be used instead of numbers. Standard
Sudoku rules apply. In addition, some
pieces are already placed into the puzzle
grid. None of these pieces is at the right
place. However, for any piece placed into
the puzzle, at least one of its
(at most
)
four edge adjacent neighbour cells must
contain the same piece in the solution as
the cell itself has in the puzzle grid.
E.g. in the sample puzzle, row 2, column 6 of the puzzle grid has a shape similar to a forward slash. This
implies that in the solution grid, at least one of the neighbours of the same cell must contain the similar shape.
Partial scoring is available in this round, depending on the number of correctly placed pieces: up to 21:
0 points, between 22-80:
(number of correctly placed pieces - 21
) * 3, 81: full score
(180 points
).
Any piece that is placed onto the grid but is incorrect, results in a deduction of 3 points
(in other words, the
number of correctly placed pieces will be reduced by the number of incorrectly placed pieces for the scoring
purposes
). If the total score is less than zero, then zero points will be awarded
(i.e. nobody will finish the round
with a negative score
).
No pencil, eraser or other marker is allowed in this round. Individual name stickers will be provided prior to
this round, competitors are kindly requested to bring it along and use them to label their solution sheets just
before this round starts."
and here is the starting picture, on which we had to put the pieces:
There are many starting points to begin the puzzle. I'd like to show that the logical path you choose could affect the difficulty of the puzzle. The point is: if you put some pieces on crucial clues, then it'll be hard to continue, because you had to raise some pieces to see important clues.
We begin by studying this piece:
The presence of such clues in R6C34 and R7C34 looks interesting. There are 2 possibilities in regions 3, 4, 7 and 8. Not very easy to see, but the same clue in R4C4 can solve the situation. These pieces must therefore be placed in R5C4, R6C2, R7C5 and R8C3.
A easier way to solve this is to look at these pieces:
![](http://img11.hostingpics.net/pics/15338425a.png)
in column 2.
The only possibility to have a neighbor for the clue in R6C2 is to put one such in R7C2
(otherwise the clue in R5C2 wouldn't have any such neighbour
). Here we are:
With the piece placed in R7C2, we can directly solved the first piece I talked about:
![](http://img11.hostingpics.net/pics/73452799b.png)
in R8C3, then regions 3, 4, 7 and 8 look like this:
Let's forget this for a while, return to starting point and concentrate on other pieces:
1rst, this one:
We can easily see that the clue in R5C1 must have a such neighbour in the solution in R6C1.
Now look at the three clues
![](http://img11.hostingpics.net/pics/33826871d.png)
in column 4.
One can easily place one such on R4C4
(neighbour for R3C4, otherwise, one of the two others will not have such neighbour
).
The situation becomes:
What is interesting with this last picture is that we hide exactly both clues that were needed to solve the clues
![](http://img11.hostingpics.net/pics/73452799b.png)
in row 6 and 7. You have now to raise pieces you've put to see these crucial clues.
So if you begin with pieces
![](http://img11.hostingpics.net/pics/47789621c.png)
and
![](http://img11.hostingpics.net/pics/33826871d.png)
, it'll will be more difficult to see the other starting point with
![](http://img11.hostingpics.net/pics/15338425a.png)
and
![](http://img11.hostingpics.net/pics/73452799b.png)
. The reverse is not true !
I think many such situations could happen while solving. If you're lucky, pieces you put doesn't hide important clues, and if you are unlucky, you get stuck and has to raise some pieces to see how to continue
(but which pieces?
).
Considering that, I asked myself if some players just studied the puzzle for a while before starting to place pieces on the puzzle and take the risk to hide some important clues.
Fred