## Where do the clues go?

Everything about Sudoku that doesn't fit in one of the other sections

### Where do the clues go?

How do you decide where the clues should be put in a puzzle? Playing with symmetry I have created two puzzles that differ only in four cells.
The puzzle below has two solutions unless there is a clue in either cell r2c3, r2c6, r3c3 or r3c6. How do I know that the puzzle is malformed if I don't put a clue in one of those cells? The solutions are:
r2c3=5, r2c6=6, r3c3=6, r3c6=5.
or
r2c3=6, r2c6=5, r3c3=5, r3c6=6.

1 2 3 4 5 6 7 8 9
9 4 _ 8 1 6 _ 2 3
8 7 _ 3 9 2 _ 1 4
7 3 4 9 2 5 8 6 1
6 9 8 7 3 1 2 4 5
5 1 2 6 4 8 3 9 7
4 5 1 2 6 3 9 7 8
3 6 7 1 8 9 4 5 2
2 8 9 5 7 4 1 3 6
howshaw

Posts: 9
Joined: 13 March 2005

I have played with changing the clues in some of the Times puzzles. There seems to be no consistancy in where they go, and although there are quotes about the symettry of the placement of clues, some puzzles have bilaterially symetric clues, others are rotationally symetric, I can't think of one with four-fold symetric clues, but I have not looked too carefully. Is there a rule? Once I found the solution for Times 15th March I took some clues out and put the correct cells for the 15th March solution in other places, but maintained symetry. When I re-solved I got a different solution! The puzzle I made could have solved to the original Times 15th March, but it didn't becaue the clues were in different places. It therefore my puzzle has at least two solutions. One is the Times 15th March, and the other is not.
Solution to 15th March as published...
813974265
679125384
425638917
147396852
982457136
536812479
791263548
258741693
364589721
If I move only 4 clues to make the puzzle as follows...
8_39_42_5
_________
42_____17
1__3_6__2
9_______6
5__8_2__9
79_____48
__8___6__
3__5_9__1

Then I can still have the original solution, but I can also have...
813974265
679125384
425638917
147396852
982751436
536842179
791263548
258417693
364589721

Cyclic permutations have occured in box 8 middle bank and in rows 5 and 6. The placement of the clues is VITAL to the puzzle, it is far more important than the underlying solution grid. Changing just a couple of clues can totally change the solution. I have tried this on many puzzles and the changes are always either pair exchanges within a row or column or cyclic permutations on three in a row or column (as here).
howshaw

Posts: 9
Joined: 13 March 2005

### This is where the clues go!

A detailed description of how to compose Su Doku puzzles is found at:
puzzle.gr.jp/show/English/LetsMakeNPElem/01
Guest

In another thread, I have remarked that these forums are entitled the Sudoku Players forums. They are not intended to be forums for puzzle setters.

This particular forum is intended to be for Sudoku solver programs, which can be used by players for assistance in solving programs.

This topic is concerned with puzzle-setting, and so to be consistent with previous policy, this topic should not be permitted in this forum. Accordingly, it will be taken down in 24 hours.

- Pappocom
Pappocom

Posts: 599
Joined: 05 March 2005

However, the question of the uniqueness of the solution to a puzzle is germaine to the construction of a solver.

In fact, I came to this forum to find information on that exact subject, and this thread is the most informtive I have seen thus far.
Guest