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
24. Doubling Investment for a Fee And Getting Zero

    Logic

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

    Arithmetic

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

    Combinatorics

46. Bicubal Domino
47. Graph with Nodes of Even Degree
48. Graph without 3-Cycles
49. Pythagorean Triples via Fibonacci Numbers

Algebra

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

    Probability

63. Average Number of Runs
64. Getting Ahead by Two Points
65. Multiple of 3 out of the Box
66. Taking Chances with Your Medicine
67. What is the Color of the Remaining Ball?

    Number Theory

68. AB × BA = 3154.
69. A Cryptarithm: A + HA = HEE
70. Diophantine Equation I
71. Primes as differences of squares
72. Simple division by 7
73. Smallest multiple of 9 with no odd digits
74. Three digit twister
75. When 3AA1 is divisible by 9?
76. When 3AA1 is divisible by 11?

    Geometry

77. Angle Bisector in Square
78. Angle in Right Triangle
79. Angle Subtended by a Diameter
80. Base and Area of an Isosceles Triangle
81. A Broken Line in 3D
82. Circle in a Square Inscribed in a Circle
83. Collinearity in Tangent Circles
84. Concurrence on a Circle
85. Construction of the Angle Bisector
86. Construction of the Perpendicular Bisector
87. Equiangular p-gons
88. Existence of the Circumcenter
89. Existence of the Circumcenter, Indirect Proof
90. Longitude, Latitude and Distance to the Equator
91. Pedoe's Theorem
92. Problem 1 from the Ninth Nordic Mathematical Contest (1994)
93. Running Lemming
94. Square in a Circle Inscribed in a Square
95. Square in a Right Triangle
96. Three Congruent Rectangles
97. Three Touching Circles
98. Triangle Areas in a Parallelogram
99. Triangle Areas in a Parallelogram II
100. Two Altitudes, One Midpoint
101. Two Equilateral Triangles
102. Two Touching Circles
103. Volume of Fibonacci Tetrahedron

     Calculus

104. The Schwarz Lantern Explained
105. Volume and Area of Torricelli's Trumpet