NOTES ON
SUDOKU CLASS #1: OCT 1 2009
1. Sudoku is pronounced: Sue Doe Coop;
silent p. No accentuated
syllable.
2. Discovered By Howard Garns,
Indianapolis; became popular in Japan;
means Su (number) and Doku (Single)
3. Not a math puzzle, but a symbol
placement puzzle; symbols: digits, colors, shapes, names of nine
grandchildren, etc
4. Sudoku contains 27 Groups
Each of 9 columns is a Group
Each
of 9 rows is a Group
Each of 9 Boxes is a Group
5. Each Group contains 9 cells
One
simple Rule: each Group of 9 cells must have a unique occurrence of each of the numbers from 1 to 9 (or whatever symbols are
being used in lieu of digits.)
6. Markup Methods: Each player must develop a personal
system for playing Sudoku; see examples on pages 1112.
Detailing: enter every possible candidate in each empty cell at the outset. Usually, on average this requires about 250 entries which are prone to errors of
omission and commission.
Parsimony: make as few entries as possible; only entries with a probability of 33% or
higher of being the correct candidate.
Muddling: somewhere in between detailing and parsimony.
7. Administration:
clerical errors the big reasons why people fail to complete puzzle
8. Guessing and Peeking for a clue are not good practices since
it destroys the flow of game. Educated
guessing OK but peek to make sure you made the right guess. Don’t worry about seeing answers to other cells.
Just do not use a “seen” number unless you can prove why it is the correct candidate.
9. The
Sudoku Unit: work at obtaining an intuitive grasp of the
Unit when you study a cell. Review page
11. Please note that the candidates for
a given cell, like the Red Cell, in the Sudoku Unit are constrained directly by every other value shown in the remaining 20 blue cells. But more importantly, the Red Cell is also constrained indirectly by the candidates that are excluded from existence in each of the
empty blue cells. A blue cell may be
empty but it contains information because it is part of a yellow Sudoku Unit
which constrains its possible candidates as well. MORE EXAMPLES OF THIS NEXT WEEK.
10. EXERCISES FROM TOP
SECRET SUDOKU SYSTEM: The book is
recommended and can be obtained from Amazon.
Describes a parsimonious markup method.
11. Page 6 top example: enter only singlets, doublets, or triplets




5 

4 

3 

1 







2 

4 

1 







(2) 
5 
(2) 
4 
1 
3 

1 

4 
4 
4 
2 
2 
2 
2 

4 

1 




12. Page 6 bottom example: enter only
singlets, doublets, or triplets

1 



2 






5 

3 




8 
2 




4 
1 

1 

(8)(4) 
(8)(4) 
2 



4 
4 
4 
5 
1 
3 
2 8 
2 8 
2 8 
(3)(5) 
8 
2 
6 7 9 
6 7 9 
6 7 9 
(3)(5) 
4 
1 
13. Page 7 example: enter only singlets,
doublets, or triplets


1 










7 
5 

4 

4 
2 
3 
8 



6 
7 
(5)(7) 
(5)(7) 
1 
4 6 2 3 
4 6 2 3 
4 6 2 3 
8 9 2 3 
8 9 2 3 
8 9 2 3 
9 6 8 
9 6 8 
9 6 8 
2 3 
7 
5 
2 3 (1) 
4 
2 3 (1) 
4 
2 
3 
8 
(1)(9) 
(1)(9) 
5 
6 
7 
Note: our discussions on this markup in class were
muddled. Normally, Brophy would view the entries of 2 and 3 in the 9 cells
above as clutter. However it is certain
that (2,4) [row 2, column4] contains either a 2 or a 3 and no other
candidates. This is important
information. The placement of the 2 and
3 in the other 8 cells adds value because all the possible candidates in boxes
1, 2 and 3 are now accounted for.
14. Question by Pysz: Can a
tripleton be placed anywhere.
Answer: on in a straight line in
the same Box.
15. McGuinness: in the
example in paragraph 12, why did you place
tripleton of 4s in box 1 before you placed the doubleton of 4s in box
2. Answer: the Force will not work the other way.
16. A cursory examination of True False Chain,
5a 



5acf 





5a 






5c 





5b 











5df 
5hi 



5cf 










5dg 



5cdi 





5ac 





5d 





5dh 




5ghi 


Assume this is all the
information we have about the 5s, and the other letters abc… represent 123..
a. if we assume the 5 in cell (2,2)[row 2 column 2) to be TRUE,
then cell (2,9) is FALSE, and then cell (4,9) must be TRUE, and then cell (6,7)
must be FALSE, and then cell (9,7) must b TRIE. and then cell (7,8) must be
FALSE, and then cell (7,2) must be TRUE.
b. But then both Cell (7,2) and Cell (2,2) are both TRUE which
is a contradiction.
c. So 5 in cell (2,2) is false and a in cell (2,2) is TRUE.
NOTES ON
SUDOKU CLASS #2: OCT 8, 2009
1. The class worked on the following
puzzle; along the way a clerical error was made which led to confusion
trying to complete the end game. The corrected unfinished puzzle is
as follows:
2.
The above puzzle stalled at the point shown above, leaving Boxes 7 and 8 in a
bit of disarray. There are at least three ways to proceed from this
juncture.
(1) Not to be silly, one can turn the
puzzle upside down, copy the red numbers and solve the new arrangement.
It may not stall. Actually this puzzle can be easily permuted into more
than a million new puzzles, all of which will be enjoyable and as challenging
as this one. The topic of rejuvenating old puzzles will be discussed next
week.
(2) The second method is to pick a cell
with two candidates. Assume one is true and the other is false.
Make small T or F notations above the candidates. Proceed to completion
or to an inconsistency. If an inconsistency is encountered then the
initial assumption was incorrect. There are certain rules that must be
adhered to. A True can imply a False, but a False need not always imply a
True. We will discuss this in class next week.
Let's assume cell (7,5) is an 8. Then the 8 in Cell (9,6) must be
False. Furthermore, the 8 in Cell (9,2) must be False. Therefore
there is no room for an 8 in row 9. Therefore the initial assumption was
incorrect. Cell (7,5) must be a 4, and from that the puzzle solves
easily.
(3) another alternative, fill in all the
possible candidates in Box 7 and 8 as shown below. And use logic to
complete the puzzle. Boxes 7, 8 and 9 are shown below to facilitate this
discussion. Using logic, the numbers that are circled can be
eliminated. This leaves Cell (9,2) as the only cell in Row 9 which
can be an 8. Assuming cell (9,2) is an 8 produces a domino effect and
solves the puzzle easily.
The logic that was
used will be discussed in class next week. The logic requires the
recognition of the following:
(a)
a naked quad in cells (7,2), (8,2), (9,2) and (1,8) which forces the
elimination of the 1 and 8 in cell (7,3)
(b)
an xywing in Cells (7,5), (7,8) and (9,4) which eliminates the 2 in cell (7,4)
(c)
an xywing in Cells (7,5), (9,2) and (9,4) which eliminates the 2 in Cell (7,6)
and the 8 in cell (9,6).
the elimination of
the 8 in Cell (9,6) forces an 8 in Cell (9,2) and the domino effect solves the
puzzle.
17. Examples of Sudoku Unit, Direct vs Indirect Constraints.
The saffron colored cell (4,4) is
indirectly constrained by cells containing 1,2,3. The Saffron Cell cannot contain any value from 1,
…..,9, so this is an illegal
configuration. Two of the white cells with candidates 1,2,3 must be
eliminated. But of course, not the
same candidate. 


The Saffron Cell is constrained
directly the candidates in the blue cells and indirectly by the three candidates
in the white cells. The Saffron Cell
can only contain a 7. 

18. fun quiz; homework; second week
NOTE: the answers in all cases is the first choice
among the given answers.
1. Sudoku (aka Su Doku) means: [single number; number puzzle; mental judo)
2. Sodoku is a: [disease, Japanese soda, Japanese word)
3. Sudoku was invented in {America, Japan,
Britain, Switzerland, Hong Kong]
4. solve this problem quickly:
you have solved a subgroup exclusion
without thinking about it
5. How many possible Sudoku puzzles
exist: [5.3 billion; 6.7 heptillion, infinite number]
6. solve this problem quickly
you have solved a hidden twin exclusion with thinking about it.
7. Solve this problem quickly
you have solved a naked twin
exclusion without thinking about it.
8. Solve this problem quickly
You have just solved a naked pair
without thinking about it.
9. Solve this problem AQAP:
10. How many ways can the digits 1, 2 and 3
be organized [6, 4,
3, 1]
11. how many ways can the digits 1, 2, 3 and
4 be organized: [24, 12, 10
12. What conclusion can you draw from the
following puzzle:
The pink cell must contain the candidate: [8,
7, 5, ≤ 4, indeterminate]
13. What value belongs in the
yellow cell: (1, 8,
6, 4)
14. what is
the legal range of values for the yellow
columns: [ (3,6,9); (1,2,3,4,6,7,9); all]
15. What candidate belongs to Cell (2,5)? (5, 1, indeterminate)
and Why?: (Force, Elimination, Guess)
16, what candidate belong to Cell (8,9)?: (9, 4, 3, indeterminate)
and Why? (Force, Guess, Naked Triple)
17. Find a starting point and fill in the Gaps:
18. Identify the Naked Pair in Row 1: [ 35; 37, 39]
Identify the Naked Triple in Row 2: [4,6,8; 6,7,8; 4,6,9]
19. What is the value of column 6: (2, 4, 5, 6)

20. What is the value of Cell(5,3) which contains: (1, 2, 8)?

NOTES ON SUDOKU CLASS #3: OCT 15, 2009
1. Homework: Read Page 22, Top Secret Sudoku System: Only pencil in the contingencies for a given object number if you can narrow its possibilities down to two contingencies in a given box, if there are three or more possibilities for a box, do not write them in.
The Brophy System makes two exceptions to the above system:
(1) write in tripletons, if they occur in a straight line within side a Box.
(2) always keep track of the number of occurrences of each number, 1,2,3,4,5,6,7,8,9. If 8 of the 9 Boxes are resolved with singletons, doubletons or tripletons, then attempt to resolve the 9^{th} Box with as many entries as needed.
2. Homework: Work through the example on Puzzle #1 on page 62. It is easy and instructive and runs through to page 77 with a tutorial.
3. Solve Example Page 7 Top Secret Sudoku System


4. Solve Example on Page 19 Top Secret Sudoku System


5. Example of a Naked Quint & Hidden Quad: Row 1 is the puzzle; Row 2 is the answer. Five cells, viz. (1,1),(1,2),(1,3),(1,8),(1,9) contain 5 values forming a Naked Quint. Therefore its values cannot exist in any other 4 cells forming a Hidden Quad, in the row.

6. Example of a Naked Quint & Hidden Quad: Row 1 is the puzzle; Row 2 is the answer. Five cells, viz. (1,1),(1,3),(1,5),(1,7),(1,8) contain 5 values forming a Naked Quint. Therefore its values cannot exist in any other 4 cells forming a Hidden Quad, in the row.

7. True/False Chain. Each cell in the chain must share a common candidate with the next cell in the chain. Proceed until completion of the chain or until an inconsistency arises. An inconsistency means that the initial assumption was incorrect. There are several paths that will work.
For example: assume candidate 1 in cell (1,1) is True. Follow the chain (1,1), (2,1), (3,1), (3,5), (2,5) (2,2) (1,2), (1,9). The chain stops because (1,1) and (1,9) both contain 1 as True. If the chain can be closed without an inconsistency, then the initial assumption was Correct.

8. An XYWing. Note that XY is the body and YZ and XZ are the Wings. Note that in both cases, when Cell (1,2) is as X or a Y, the cells with O in it cannot contain a value of Z.

9 XYWing Illustration: Find the XY Wing? The XYWing is made up of cells (1,6), (1,7).(9,7)

10. Work on puzzle 005304800…. on page 16 in Senior Sudoku.
11. keys (explain keys: the following string of 81 numbers represents a puzzle, starting in cell (1,1) and working left to right and down the page, ending on cell (9,9)
chain puzzles 537060249018002000290070008060507020050020080020604590970000002085200970142739865
This puzzle has multiple solutions but excellent example of the use of advanced methods.
We will solve this puzzle in class using on line internet tools.

537060249018002700290070008060507020050020080020604590970000002085200970142739865
This puzzle is solvable, but difficult, but contains good examples of advanced tools. We will solve in class using online internet tools.
