今年puzzleup还没消息

〇〇

要开始了
Puzzleup 2022 will commence on the 19th of October 2022 at 11:00 (GMT). The competition will last 10 weeks, and every week a question prepared by Emrehan Halici will be posted on www.puzzleup.com website. We invite puzzle lovers all over the world to our online PuzzleUp competiton. Best luck to all.

jihuyao

I guess I can conclude the sudoku topic discussion in certain encouraging way.  After some further exploration on 2x2, I realized the math expression underneath is a few groups of bitmap interfering each other, eg, 2**a11+2**3+2**a13+2**1=2+4+8+16.  It is so obvious and simple that I have to pulse for a while and ask if all has similar sets of bitmap group expressions why some are easy to solve and some are not?  Without further on 3x3 I predict (if I may) that if more unknowns involves in all diagonal box groups (eg, 1/5/9, 1/7/6, etc), the harder to solve it.  One can build up all diagonal box bitmap expression using all given constraints on row, col and box.  If possible math guy may obtain the sole solution through derived diagonal box bitmap expression without using those sudoku logical skills.  If not one can still play probably one one trial and error by cutting the link of ONE cell which involves the most groups of diagonal box bitmap expressions.  When all long diagonal box bitmap expression is cut several small pieces of expression, it would be possible to solve the problem easily using those logical skill like single/double/triple/x-wing/...  So it is my conclusion in topic 2, no more blind cat catching dead rat.  With those bitmap expressions one may figure out some logical skills for those hard sudoku problems containing long range linking.  Now we may go a little deep on topic 3.  Or we should ask the question differently.  For all given diagonal box combinations (which are equivalent through all transformations), the minimum number of known cells is the same (very likely)?  But for different equivalent combinations, the minimum is still 17? To me it is unlikely because logically if given combination leads more possible solutions it should need more known cell to narrow down to one solution.  At least, not all those equivalent combination has the same minimum value.  Finally, if I may, I would say the topic 1 is worth a BS thesis, and topic 2 worth a couple of MS thesis, and topic 3 worth a few or several PhD these.  Purely in math it still worth deep studies on those complex, multiple group of interfered bitmap expressions, eg the sufficient conditions for any given expression may lead to only one solution (the expressions look like primary level algebra but solution definitely is not so simple.