2. Whiteboardmaths.com © 2008 All rights reserved 5 7 2 1

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

4. 6 1 8 4 7 9 2 5 3 5 6 1 8 3 2 7 9 4 4 9 7 6 5 1 8 3 2 8 3 2 4 7 9 5 1 6 5 4 9 1 2 3 7 6 8 7 2 3 6 5 8 1 9 4 3 4 7 1 2 6 9 8 5 2 8 5 9 7 4 3 1 6 9 6 1 3 8 5 2 4 7 The object of this number game is to place the digits 1 to 9 in each 3 x 3 box in such a way that the numbers 1 to 9 also appear in each row and column of the large 9 x 9 grid. The levels of difficulty can vary from fairly straight forward to fiendishly difficult.

5. SUDOKU In the more difficult puzzles there are many occasions when two or more possible numbers can go in each cell and you will usually have to pencil these possibilities in, in small writing before deciding which goes where later. Before this stage there are always some cells that can have a single solution. It is better to try and find all these solutions first, before moving on to cells that have multiple possible solutions. 6 8 7 2 3 6 5 1 2 8 3 2 7 1 3 5 1 4 4 2 8 2 9 7 4 8 9 5

6. Tips for solving SUDOKU 6 8 7 2 3 6 5 1 2 8 3 2 7 1 3 5 1 4 4 2 8 2 9 7 4 8 The squares indicated in red cannot contain a 2, hence we have our first solution. 2 9 5 We will look at the puzzle shown which gives us 28 completed cells and discuss some of the methods of finding the numbers that go in some of the blank cells.

7. SUDOKU 6 8 7 2 3 6 5 1 2 8 3 2 7 1 3 5 1 4 4 2 8 2 9 7 4 8 A similar situation occurs with the highlighted 8’s forcing our second solution. 2 8 9 5

8. SUDOKU 6 8 7 2 3 6 5 1 2 8 3 2 7 1 3 5 1 4 4 2 8 2 9 7 4 8 2 8 Row 2 needs an 8 but it can’t go in the red cells. 8 9 5

9. SUDOKU 6 8 7 2 3 6 5 1 2 8 3 2 7 1 3 5 1 4 4 2 8 2 9 7 4 8 2 8 Row 2 needs a 9 and a 4 but a 4 cannot go here so we have 2 more solutions. 8 4 9 5

10. SUDOKU 6 8 7 2 3 6 5 1 2 8 3 2 7 1 3 5 1 4 4 2 8 2 9 7 4 8 2 8 8 4 9 4 9 5

11. 6 8 7 2 3 6 5 1 2 8 3 2 7 1 3 5 1 4 4 2 8 2 9 7 4 8 2 8 8 9 4 2 9 5 4

12. 6 8 7 2 3 6 5 1 2 8 3 2 7 1 3 5 1 4 4 2 8 2 9 7 4 8 2 8 8 9 4 2 2 9 5 4

13. 6 8 7 2 3 6 5 1 2 8 3 2 7 1 3 5 1 4 4 2 8 2 9 7 4 8 2 8 8 9 4 2 2 2 9 5 4

14. 6 8 7 2 3 6 5 1 2 8 3 2 7 1 3 5 1 4 4 2 8 2 9 7 4 8 2 8 8 9 4 2 2 2 7 9 5 4

15. 6 8 7 2 3 6 5 1 2 8 3 2 7 1 3 5 1 4 4 2 8 2 9 7 4 8 2 8 8 9 4 2 2 2 7 9 5 4

16. 6 8 7 2 3 6 5 1 2 8 2 7 1 3 5 1 4 4 2 2 9 7 8 2 8 8 4 9 4 2 2 2 7 5 Trickier situations 3 7 In this 3 x 3 box there are two cells that are not filled in as they could take either a 3 or a 7. How can we decide? 3 3 These 3’s hold the key. 3 7 This forces the entry in this cell to be a 7 and the other to be a 3. 5 6 None of these red cells can be a 3, thus forcing the remaining cell to be a 3. 3

17. SUDOKU 6 8 7 2 3 6 5 1 2 8 2 7 1 3 5 1 4 4 2 2 9 7 8 2 6 8 4 9 4 1 2 2 7 5 Trickier situations. In this 3 x 3 box there are two cells that are not filled in as they could take either a 3 or a 7. How can we decide? 3 3 These 3’s hold the key. This forces the entry in this cell to be a 7 and the other to be a 3. 5 6 3 7 3 None of these red cells can be a 3, thus forcing the remaining cell to be a 3.

18. Puzzle 1 368712594 724859163 159634287 431578926 895326741 672491835 543987612 286145379 917263458 Fairly EasyPuzzle 1 Solution > Getting Started Usually a sudoku becomes trickier when less “start numbers” are given but don’t take this as a general rule. There are also hard sudoku’s with many start numbers given, and easy ones with only a few start numbers given. 38 start numbers Worksheets >

19. Fairly EasyPuzzle 1 Puzzle 2 > 368712594 724859163 159634287 431578926 895326741 672491835 543987612 286145379 917263458 Getting Started Usually a sudoku becomes trickier when less “start numbers” are given but don’t take this as a general rule. There are also hard sudoku’s with many start numbers given, and easy ones with only a few start numbers given. 38 start numbers

20. Puzzle 2 MediumPuzzle 2 Solution > 983475126 457621389 621938457 145786293 792543861 836192574 278364915 564219738 319857642 Getting Started Usually a sudoku becomes trickier when less “start numbers” are given but don’t take this as a general rule. There are also hard sudoku’s with many start numbers given, and easy ones with only a few start numbers given. 35 start numbers

21. MediumPuzzle 2 Puzzle 3 > 983475126 457621389 621938457 145786293 792543861 836192574 278364915 564219738 319857642 Getting Started Usually a sudoku becomes trickier when less “start numbers” are given but don’t take this as a general rule. There are also hard sudoku’s with many start numbers given, and easy ones with only a few start numbers given. 35 start numbers

22. Puzzle 3 HarderPuzzle 3 Solution > 312549768 749168523 865327419 654781392 128493657 937256841 573612984 481975236 296834175 Getting Started Usually a sudoku becomes trickier when less “start numbers” are given but don’t take this as a general rule. There are also hard sudoku’s with many start numbers given, and easy ones with only a few start numbers given. 31 start numbers

23. HarderPuzzle 3 312549768 749168523 865327419 654781392 128493657 937256841 573612984 481975236 296834175 Getting Started Telegraph > Usually a sudoku becomes trickier when less “start numbers” are given but don’t take this as a general rule. There are also hard sudoku’s with many start numbers given, and easy ones with only a few start numbers given. 31 start numbers

24. Telegraph Puzzle ModerateDaily Telegraph Puzzle Solution > 968425731 352791468 417863592 246187359 789536214 135942687 521678943 693214875 874359126 Generally, Sudoku puzzles in daily newspapers are harder than the three introductory ones given earlier. As the puzzles increase in difficulty you may wish to learn other strategies to help you solve them. You can download a “solving sudoku document” at: http://www.sudoku.org.uk/ It is not unusual to spend ½ to 2 hours on some puzzles. 26 start numbers

25. ModerateDaily Telegraph Puzzle 968425731 352791468 417863592 246187359 789536214 135942687 521678943 693214875 874359126 Generally, Sudoku puzzles in daily newspapers are harder than the three introductory ones given earlier. As the puzzles increase in difficulty you may wish to learn other strategies to help you solve them. You can download a “solving sudoku document” at: http://www.sudoku.org.uk/ It is not unusual to spend ½ to 2 hours on some puzzles. 26 start numbers

26. Number of Solutions How many ways are there of filling a blank 9 x 9 grid with the numbers 1 to 9 according to the rules of the game? In other words how many solutions are there? 968425731 352791468 417863592 246187359 789536214 135942687 521678943 693214875 874359126 Some Sudoku Questions

27. How many ways are there of filling a blank 9 x 9 grid with the numbers 1 to 9 according to the rules of the game? In other words how many solutions are there? 968425731 352791468 417863592 246187359 789536214 135942687 521678943 693214875 874359126 1 Solution 968425731 352791468 417863592 246187359 789536214 135942687 521678943 693214875 874359126 Mathematicians have shown that there are: 6,670,903,752,021,072,936,960 (6.67×10 21 ) different solutions. Some Sudoku Questions

28. Minimum Entries What is the smallest number of cell entries that a puzzle can have so that it yields a unique solution. Some Sudoku Questions 968425731 352791468 417863592 246187359 789536214 135942687 521678943 693214875 874359126 26 start numbers “At the moment, there are examples of 17-hint uniquely completable Sudoku puzzles, but no known 16-hint examples. Hence I am collecting as many 17-hint examples as possible, in the hope that their analysis will yield some insight. Currently I have a collection of 47793 distinct Sudoku configurations with 17 entries”. Gordon Royle, The University of Western Australia. http://people.csse.uwa.edu.au/gordon/sudokumin.php 968425711 352791468 427863592 246157654 788536214 131992387 321478243 693114875 875857126

29. Worksheet Fairly Easy Medium Harder 368712594 724859163 159634287 431578926 895326741 672491835 543987612 286145379 917263458 983475126 457621389 621938457 145786293 792543861 836192574 278364915 564219738 319857642 312549768 749168523 865327419 654781392 128493657 937256841 573612984 481975236 296834175 968425731 352791468 417863592 246187359 789536214 135942687 521678943 693214875 874359126 Daily Telegraph (Moderate)