High School Problem Archive

* Denotes a problem for which no solution has been submitted.
A problem whose solution has recently been posted is indicated with a +.
  1. Counting Intersection Points
  2. Find the Unknown Area
  3. Rearranging Digits
  4. What's the Locus?
  5. Egg Drop Soup
  6. The Moat
  7. The Pane of it All
  8. A Magic Square
  9. Reflections
  10. A Problem from Lewis Carroll
  11. Drawing a Zigzag through 16 points
  12. How Big is the Softball?
  13. What's the Radius of the Circle?
  14. A Belt Around a Pulley
  15. What's the Area of the Hexagon
  16. How Long Will the World Series Last?
  17. What's the Area of the Wedge?
  18. Find the Dimensions of the Rectangle
  19. Move the Last Digit to the Front
  20. A Pyramid of Cubes
  21. Reverse the Digits
  22. Two Circles in Two Triangles
  23. Dissecting Squares and Cubes
  24. A Sum of Two Reciprocals
  25. Travels with a Canoeist
  26. Those Crazy Mathematicians
  27. Polygons Inside Circles Inside Polygons
  28. What are the Kids' Ages?
  29. Use Each Nonzero Digit Once
  30. Product of Cosines Equation
  31. A Stack of Balls
  32. A Magic Hexagram
  33. How Many Digits Does It Take?
  34. A Putnam Problem
  35. Infinite Nested Radical
  36. Does Your Cup Runneth Over?
  37. A Box of Valentine's Candy
  38. Locker Lottery
  39. David Hilbert's Birthday
  40. Height of an Octahedron
  41. Size of the Block?
  42. Polygonal Partitions
  43. Digital Divisors
  44. Another Nested Radical
  45. Some Divisibility Tests
  46. The Difference of Two Squares Being a Cube (Putnam)
  47. A Clock Puzzle from "Car Talk"
  48. The Area of a Heart
  49. An Area Ratio
  50. The Initial Digits of N Cubed are the same as N
  51. More Fun with Digits
  52. What's the Ratio of Squares' Areas?
  53. Find the Length of the Triangle's Side
  54. Four Similar Rectangles
  55. An (Almost) Regular Octagon
  56. A Trapezoid with Perpendicular Diagonals
  57. The Spider and the Fly
  58. Alice and Bob and the Three Denominations
  59. How Many Paths from X to Y?
  60. Area of a Cyclic Quadrilateral
  61. Area of a Trapezoid
  62. Sums of Consecutive Integers in Several Ways
  63. Packing Five Spheres in a Box
  64. A Cryptarithm ("Sam's Idea")
  65. Finding a Cube Ending in Consecutive Digits
  66. Five Tangent Circles
  67. Five Numbers in Geometric Progression
  68. A Ratio of Lengths in a Triangle
  69. A Circle in a Sector
  70. How Much Does the Mozzarella Weigh?
  71. Solve the Nonlinear System of Equations
  72. A Circle and a Square in a Circle
  73. Find the Radius of the Circle
  74. Use Each Digit Exactly Once
  75. A Quasi-Magic Triangle
  76. Compute the Length of a Rod from the Length of its Shadows
  77. A Japanese Junior High Entrance Exam Question
  78. What has the Same Value as MATH?
  79. Multiples Whose Digits are All 1's and2's
  80. Find the Tetrahedron's Volume
  81. A Tribute to Martin Gardner
  82. Find the Inner and Outer Radii of the Annulus
  83. A Palindromic Square
  84. Find the Village's Population
  85. Three Circles, a Triangle, and a Rectangle
  86. Three Circles in a Semicircle
  87. Four Semi-circles in a Square
  88. Find the Area of the Triangular Pieces
  89. A Cryptarithm
  90. Decreasing Numbers
  91. Find the Radii of the Circles
  92. How Many Equidistant Planes are There?
  93. Find the Missing Number
  94. A Magic Pentagram (Revised)
  95. Packing Two Circles in a 3-4-5 Right Triangle
  96. A 4×4 Array of 1's and −1's
  97. A Quincunx in a Circle
  98. Dividing Lines with Side-Trisectors
  99. A 3-4-5 Triangle in a Square
  100. Find the Largest Power of 2006 that Divides 2006 Factorial
  101. Numbering the Vertices of a Cube with No Consecutive Numbers Adjacent
  102. A Diophantine Equation +
  103. A Formula for the Area of a Face of an Ortho-Simplex +
  104. A Point in a Square +
  105. A System of Equations +
  106. A Broken Pole +
  107. When are You Unable to Make Change? +
  108. An Exponential Equation +
  109. Quadrisecting a Square +
  110. Five Similar Rectangles +
  111. A Fibonacci Question
  112. Five Circles in a Square
  113. A Circle Inscribed in a Triangle Inscribed in a Circle
  114. Dissecting an Isosceles Triangle into Two Isosceles Triangles
  115. A Circle Internally Tangent to Three Others
  116. How Long Does It Take to Do the Job?
  117. Find the Polynomials (Putnam)
  118. Happy New Year, 2008
  119. Rationalize the Denominator
  120. In How Many Ways Can You Write {1,...,7} as the Union of Two Sets?
  121. A Drawer Full of Socks

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