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2.Cutting Wood Logs                                                                                                            8

3. Plant Trees                                                                                                              11

4. In Which Column Is n                                                                                            15

5. Crossing Numbers                                                                                                   23

6. How Many Tiles Will It Cross                                                                                26

7. How Many Ways to Walk                                                                                      31

8.Number of Divisors                                                                                                 38

9. Number of Square Divisors                                                                                    42

10. Hand Shakes                                                                                                         46

11. Diagonal and Angles of Convex Polygons                                                           53

12. Last Digit                                                                                                              58

13.Pick's Law                                                                                                             62

14. The Area of Rectangle                                                                                          66

15. Net of A Cube                                                                                                      70

16. Net of An Octahedron                                                                                          74

17. Sum of All Digits                                                                                                  79

18. Sum of Numbers by Permutations of Digits                                                         84

19.Greatest Value Not Attained                                                                                89

20. Number Separation                                                                                               97

21. Counting Lines                                                                                                     104

22. Counting Angles                                                                                                   110

23. Counting Points                                                                                                    114

24. Counting Triangles With Lines                                                                             120

26. Counting Rectangles With Lines                                                                          133

27. Counting Rectangles With Dots                                                                           142

28.Counting Solids                                                                                                    149

29. Cutting Regions by Simple Figures                                                                      154

30. Counting Regions by Combined Figures                                                              161

31. Triangulation of  Shapes                                                                                       167

32. Digits Arrangement                                                                                              173

33.Page Numbering                                                                                                   180

34. How Many Faces Are Painted                                                                              183

35. Tailing Zeros                                                                                                         186

37. Factoring Tricks                                                                                                    195

38. Denesting Square Root                                                                                         201

39.

Index                                                                                                                          219

Yongcheng Chen is an environmental engineer with a Ph.D. degree in Engineering.

Jane Chen is a sophomore at Stanford University. She is the author of the recent publication by Mathcounts Foundation:  “The Most Challenging Mathcounts Problems Solved”.