serban from cluj

Hello Serban - welcome to the Sudoku site.
Is Cluj a city in Romania? If so, it looks a wonderful place full of history.

Serban! Hope you have a lovely birthday.

Hope you have a very Happy Birthday, Serban!

Well, another birthday comes your way, Serban!
Enjoy your special day.

Best wishes for a very Happy Birthday!

Happy Birthday! I decided to do a search on Cluj and learned so much today.

Searching algorithm
1. For each candidate -digit will be determined the cells in which the candidate
can take values.
In this way we’ll obtain nine 9x9 matrix m1, m2, …, m9 with n1, n2, …. ,n9 candidates
with k1, k2, …, k9 lines, columns, blocks unfilled
2. The next step consists in calculus of numbers of possible cases- Nc
3.For each case will be verify the accomplishing of bases conditions(necessary constraints)
If these conditions are accomplished, from the unsolved cells,
the candidate or candidates (if exists) will be eliminated.
Annotation
C(N,k) - Combination of N taken by k
Nc- number of possible cases
N- number of unresolved (empty) cells
N2- number of unresolved cells - occupied by 2 candidates -bivalue cells
N3- number of unresolved cells -trivalue cells
N4- number of unresolved cells -quatrovalue cells
N=N2+N3+N4+...+N7
%---------------------------------------------------------
Below are presented the few examples
1 digit pattern
X-chain Nci= C(ni,ki) i=1:9
Note
1.In order to keep the computing time in range of few seconds,
ni must be lower than 30 ni<=30
2. X-chain can replace the techniques included in
the fish strategies(Basic Fish,kite,skyscaper,etc)
Basic Fish
X-wing Nci= C(ki,2) maxim ki=9 => Nci=36
SwordFish Nci= C(ki,3) maxim ki=9 => Nci=84
JellyFish Nci= C(ki,4) maxim ki=9 => Nci=126
%--------------------------------------------------
2 digit pattern
W-wing Nc=C(N2,2)
XY-wing Nc=C(N2,3)
%--------------------------------------------------
3 digit pattern
XYZ-wing Nc=C(N2+N3,3)
UR-type 1,2 Nc=C(N2+N3,4)
%-------------------------------------------------------
4 digit Pattern
XYZW-wing Nc=C(N2+N3,4)
XY-chain-4 Nc=C(N2,4)
Sue de Coq 4 Nc=C(N,4)
UR-type 3-6 Nc=C(N,4)
%-------------------------------------------------------
5 digit Pattern
Sue de Coq 5 Nc=C(N,5)
XY-chain-5 Nc=C(N2,5)

Thanks serban, that's a great help for me.

Solving algorithm

Each unsolved Sudoku game is a 9*9 'S' matrix with 81 partially occupied cells
N cells occupied, E=81-N unoccupied cells
Each solved Sudoku game
- N=81 E=0
- each row, column and box contains all the numbers 1 to 9. n=9 e=0

Matrix S contains 36 matrices u with 9 partially, fully or unoccupied cells
( 9-row 1*9,9-column 9*1,9-box 3*3,9-number )
Program=basic techniques+ X-wing ,X-chain,W-wing,XY-wing ,XY-chain ,XYZ-wing

The program determines the numbers that can occupy each free cell
In each free cell there are 2 or more numbers
%======================================
1. Choose a partially occupied 'u' matrix n<=7 e=9-n
2. From 'u' we obtain - more-Nc- matrices 'u1' fully occupied n=9 e=0
3. For each case, enter u1 (the fully occupied matrix) in the S matrix.
Result Nc matrices S1 with N+9-n =N+e occupied cells
4. The matrix S1 is -analyzed- solved with the same program, one of the cases Ns <= Nc
being the solution of the game

Hello Serban, I have just read in our local paper about a man from Romania playing cricket and coaching in our local team in Albany and it mentioned that his local side is Cluj Cricket Club in the European Cricket League. His name is Pavel Florin.

Serban. Enjoy your special day celebrating with family and friends.