Thursday, October 22, 2015

This 'n That Thursdays: Scary Sudoku!

From Improve Concentration Information

With Halloween so near, I was trying to come up with a scary topic for this week's post, when it suddenly occurred to me that few subjects are more frightening than numbers!  So this week's post is all about sudoku, that diabolical number puzzle consisting of a large square divided into nine smaller squares.  Each of these medium-sized squares is then divided into nine more squares.  The object of the game is to fill each of the medium-sized square's small squares with the numbers one through nine, such that each number is only used once in each medium-sized square as well in as each row and column of the large square.  Some of the small squares are already filled in, and the difficulty of the sudoku depends upon how many clue numbers are already given.

Got that?  If not, then let's start with an even easier type of sudoku, which consists of four medium-sized squares containing four small squares:

Remember that each of the small squares in each medium square, row, and column cannot repeat any of the numbers 1 through 4.  For example, look at the first column.  There is a 4 in the second small square down and a 3 in the third small square down, so that means the square at the top cannot be a 3 or a 4.  If you look at the first row, the numbers 1 and 4 occur in the second and fourth small squares, so the number 1 is also eliminated.  Therefore, the top left small square number has to be a 2!  That means the bottom left small square number can only be a 1, and the first column is complete.

Now look at the first and fourth rows.  They are only missing one number each, and are easily filled in, which then also completes the third column. Row two contains the numbers 4 and 1 in the first and third small squares, so a 2 and 3 are needed.  Column two already has a two in a small square, so the second small square gets a 3, leaving the 2 for the fourth one.  Now columns two and four are only missing one number and are quickly filled in, which also completes row three.  The numbers for the rows, from top to bottom, are:

2   1   3   4
4   3   1   2
3   4   2   1
1   2   4   3

And the puzzle is done!  How simple was that?

Ready to attempt the real thing?  If so, here is an easy example (it will be easier to fill in the puzzle if you print out a copy or make your own grid and fill in the numbers already given):

From Sudoku Instructions

Don't panic!  This sudoku even has a labelled grid system, so I will refer to the small squares by their grid numbers when I can.  Also, each medium-sized square is represented by a large capital letter (J through R) and I will refer to these squares by their capital letter if possible.  I usually start a sudoku by looking at rows and then columns.  If you look at the first three rows (1-3 on the grid), you will notice that there are three 9s, one in each medium-sized square (J through L).  This means you do not have to worry about the 9s!  Now check the 8s.  There is an 8 in the J and K squares, but none in L.  Since the 8s are in rows one and two, the third 8 must be in row three.  Scanning down each column in L (G, H, and I on the grid), notice that H-3 already has a number and there is already an 8 in column G at G-7.  Obviously the 8 for square L belongs in I-3!  Try this same method with the numbers 7, 3, and 2 and it is even easier, as there is only one square available for 7 (I-2), 3 (C-1), and 2 (G-3).

Move on down to the next three rows (4-6) and try the same technique with the numbers 9, 8, 7, and 1 (the number 4 is already done).  Then do the same thing for the last three rows (7-9) with the numbers 9, 6, and 4 (notice that there are also two 5s, but this method will not work because there are two available squares for the last 5).  Now go to the columns and start the method over with the first three (A-C) for 7.  Then on to the next three columns (D-F) for 8, 5, and 4.  Finally, do the last three columns (G-I) for 4 and 2.

There are a couple of ways to proceed from here.  You can start all over again with the rows and then columns, because so many squares are now filled that the options for the empty squares are fewer.  For example, you can now fill in a 4 at A-2.  Your other option is to now look at each of the medium-sized squares (J-R) to see if you can fill anything in.  For example, look at square L.  There is only one empty small square!  Every number has been used except 5, so now you know that 5 goes in I-1.  Pretty simple, right?  Do the same thing with each row and column.  If only one square is empty, then you know that the only number not yet entered goes into that small square (try row 1 as an example).

Using a combination of these two methods will eventually get all of the small squares filled, and you are done!  If you find that two small squares are empty, remember to check the medium-sized square, row, and column associated with each small square to see if either number has already been used in any one of those three places.  If one has, then it is the number not found that is the correct choice.  For example, as you get to the end of the sudoku, you may have two empty small squares in the third row, A-3 and B-3, and the numbers 5 and 6 are missing.  If you look down column A you will find a 5, so put the 6 in A-3, which means that 5 goes in B-3.  Here is the final result:

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

Phew!  That took a while to explain.  I am sure you are totally confused now, but really the best way to learn sudoku is to just do it.  I have never been fond of numbers and never thought I would like sudoku puzzles, but one day I decided that the only way to get over my number phobia was to simply plunge right in.  I bought a couple of sudoku puzzle books, started at the beginning, and tried to work my way through to the end.  I do get stuck occasionally, but on the whole I can finish most of the easy and moderate sudokus.  I am still working on the difficult ones, but the more I do the quicker I get at figuring out the solutions.  At first you may need to write out the possibilities before choosing the right number, but after a while I was able to do this in my head (at least for the less difficult ones), so I feel I really have conquered my number phobia to some extent.  One of these days I might even be ready to tackle KenKen, another type of math puzzle that adds simple arithmetic into the equation (ugh, pardon my pun!).

Puzzles and games like sudoku are supposed to be good for mental agility, especially as we age.  If you would like to try solving a sudoku puzzle, check out the puzzle site here.  You can choose the difficulty level, and the game will give you all sorts of encouragement along the way as well as keep track of which number you are working on and how many squares are filled in.  There are many sites on the internet attempting to explain how to work a sudoku puzzle, such as the ones here and here, so if you get stuck or confused just do a search for sudoku instructions for beginners and you may find more helpful tips.

If you don't give sudoku puzzles a try because you find them far too scary, then I suppose you can just consider them another Halloween fright!

From Increase Sales Blog


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