Red Ed wrote:I've mailed him, seeking clarification.

Thanks for the mail. Glad to be of help.

Clarification in reponse to Gordon's post on Feb 11: I'm afraid the following sounds extremely pedantic, but if I put it down like this, I think I won't make a mistake.

The following definitions are made for any fixed puzzle (ie, a puzzle with given clues)

1) Elementary propositions in Su Doku are "B contains {N}" or "B does not contain {N}" (where B is a box and N is a number). Compound propositions, which are unions of simple propositions such "B contains one of {N1,N2,...} and none of {M1,M2,...}" are less interesting for this definition.

2) In a proper Su Doku, all elementary propositions are provably true or false, given the clues. (This defines proper Su Doku).

3) In a good Su Doku exactly one of the 9 elementary propositions of the form "B contains {N}" is true for each B, given the clues. (This is a definition of "good Su Doku").

4) Some elementary propositions are true or false because the box they refer to contain a clue. Such statements are "trivial propositions" (either trivially true or trivially false).

Now the definition of a maximum Su Doku:

5) If a good Su Doku remains a good Su Doku after removal of a clue, then that clue is called a derivable clue.

6) Removal of all derivable clues from a good Su Doku leads to an irreducible Su Doku. (Any irreducible Su Doku is a good Su Doku, by this definition)

7) The set of irreducible Su Dokus with maximum number of clues is called a maximum Su Doku.

8) The set of irreducible Su Sokus with minimum number of clues is called a minimum Su Doku.

In other words, I agree with Moschopulus, provided that the definition of minimum on the forum is the same as my definition of irreducible above. I would prefer to call a puzzle irreducible (or good but reducible), and reserve the words minimum and maximum for counts of the number of clues.

MCC's post of Feb 11 contains a good example of what I mean by an elementary proposition in (1) above and proceeds to give an example of what I call a proof or derivation in (2) above.

The maximum Su Doku example in

http://theory.tifr.res.in/~sgupta/sudoku/expert.html is an impostor for the two reasons already noticed on the forum: it is not a good Su Doku (as pointed out on Feb 12: 6 does not fit into the center 3X3 box) and the Su Doku is not irreducible, Thanks for checking this; I'll modify the figure on the web page with acknowledgements to this thread.

The best that I can dash off quickly is the 29 clue irreducible Su Doku:

..3|..6|78.

.56|.8.|12.

78.|.2.|.5.

---+---+---

.7.|34.|...

364|8..|...

...|2.1|...

---+---+---

6.2|.14|...

81.|...|...

...|5..|...

This has more clues than the example MCC gives in his post of Feb 11 (or in the three irreducible versions of that problem which are given by gsf, although I haven't checked their irreducibility myself).