Fill-It-In Outline Mathematics

Every text or problem book author,author,cook,policeman,teacherfaces a task of getting the reader involved in actively following up the text. Learning mathematics is necessarily an active pursuit of knowledge. Many a stratagem have been devised to achieve the goal of enticing the student into the right mood and attitude. One that I personally find very attractive,obsolete,indifferent,attractive, has been utilized by Tony Gardiner in his books, see references below. The gist of his outline solution approach is in supplying almost complete solutions to every problem with crucial pieces of information omitted now and then. The reader - a student - is made to follow and learn from the logic of the mentor and also pass local tests of his or her grasp by filling in the missing pieces.

The problem collection below is an attempt to master the outline solutions approach in the dynamic on-line setting.

Most of the samples below can be classified as Word Problems, i.e. problems presented in a verbal form, which, in order to be solved, should be translated into the mathematical language. Several tutorials for such a translation are provided elsewhere.

Word Problems

1. A Freeloader
2. A Word Problem with Pens and Pencils
3. Abdul and 10 Thieves
4. Billy is twice as old as Sally
5. Cars and motorcycles
6. Child and Adult Ticket Count
7. Coin counting word problem
8. Constrained Intermarriages
9. Crab's Weight
10. Diluted Paint
11. Five siblings
12. Half an egg wonder
13. How old is Al?
14. How old is Karen?
15. Lemons by Dozen
16. Problem #24 from the Rhind Papyrus
17. Sweet Purchase
18. The ass and the mule
19. The lucky find
20. The Number of Judges and the Number of Votes
21. Thirty Clerks
22. When Son Will Catch Father?
23. Train on Bridge

    Logic

24. Elves and Gnomes
25. Knights and Knaves #1
26. Knights and Knaves #2
27. Knights and Knaves #3
28. Robbery #1
29. Robbery #2
30. Robbery #3
31. Robbery #4
32. Sons and Fathers
33. Who Has the Beard?

    Arithmetic

34. Food of a Lifetime
35. Grandfather's Bill
36. Insect flight record
37. Is GLOBALHELLFRY a Prime?
38. M. Jordan and K. Abdul-Jabbar
39. "Math trick" with two dice
40. Mathematicians and Musicians
41. Planeload
42. Practical Relativity
43. Two Consecutive Numbers with Small Sum
44. Billiard Handicap

    Combinatorics

45. Bicubal Domino
46. Pythagorean Triples via Fibonacci Numbers

Algebra

47. A Cryptarithm for Middle School
48. A Typical Age Problem
49. Advancing a Millenium Problem
50. All Powers of x are Constant
51. Filling Pool with Fluids
52. Four Weighings Suffice
53. Getting Your Rightful Share Back
54. Improving on an Escalator
55. Inequality with Logarithms
56. Rabbits Reproduce; Integers Don't
57. Ratios and Sharing
58. Train on Bridge

    Probability

59. Multiple of 3 out of the Box
60. What is the Color of the Remaining Ball?

    Number Theory

61. AB × BA = 3154.
62. A Cryptarithm: A + HA = HEE
63. Diophantine Equation I
64. Primes as differences of squares
65. Simple division by 7
66. Smallest multiple of 9 with no odd digits
67. Three digit twister
68. When 3AA1 is divisible by 9?
69. When 3AA1 is divisible by 11?

    Geometry

70. Angle in Right Triangle
71. Angle Subtended by a Diameter
72. Base and Area of an Isosceles Triangle
73. Circle in a Square Inscribed in a Circle
74. Concurrence on a Circle
75. Construction of the Angle Bisector
76. Construction of the Perpendicular Bisector
77. Existence of the Circumcenter
78. Existence of the Circumcenter, Indirect Proof
79. Longitude, Latitude and Distance to the Equator
80. Pedoe's Theorem
81. Running Lemming
82. Square in a Circle Inscribed in a Square
83. Square in a Right Triangle
84. Three Congruent Rectangles
85. Three Touching Circles
86. Triangle Areas in a Parallelogram
87. Triangle Areas in a Parallelogram II
88. Two Altitudes, One Midpoint
89. Two Equilateral Triangles
90. Two Touching Circles

    Calculus

91. The Schwarz Lantern Explained
92. Volume and Area of Torricelli's Trumpet