× Denotes a partially solved or open-ended problem.

o Denotes a work in progress.

+ Denotes a problem whose solution has recently been posted.

- A Bitangent to a Quartic Curve
- Minimizing the Area of a Parabolic Sector
- Finding the Height of a Mountain
- A Circle Bitangent to a Parabola
- The Area and Perimeter of a Certain Region
- An Incorrect Quotient Rule for Derivatives
- Which Value of
*a*Gives a Unique Solution? - Finding the Area (resp. Volume) of Overlapping Circles (resp. Spheres)
- Expected Area of an Inscribed Triangle
- The Limit of a Harmonic Sum
- Maximize the Area Between a Circle and a Polygon
- Maximize the Total Surface Area of an Inscribed Cylinder and Cone
- Two Infinite Series
- The Number of Solutions of a Trigonometric Equation
- Drilling a Cube
- Overlapping Tangent Parabolas
- Surface Area and Volume of a Pendant
- Minimize the Arclength
- When Does the Sum Get Big?
- Two Leibnizian Infinite Series
- A Product of Cosines Equation
- Minimizing the Perimeter of a Parabolic Region
- Half Full or Half Empty?
- A Putnam Problem
- Intersecting Cylinders, Part I
- Intersecting Cylinders, Part II
- A Heart-Shaped Box
- Probability of Making a Triangle
- Maximize the People-Days
- Making a Planter
- What's the Average Width?
- Turning the Corner with a Rod
- Putting a Sphere in a Cone
- Average Size of a Piece of a Broken Stick
- Rotating Reuleaux
- Find the Limit of the Sum (Putnam)
- The Average Distance Between Points in the Cantor Set
- Put the Heart in a Box
- Where Does the Spiral End?
- What Shape Does the Sliding Rod Trace Out?
- The Expected Area of a Triangle
- Another Limit Problem
- Find the Area of the Deltoid
- Two Cyclists
- Three Circles in a Parabola
- A Circle Perpendicular to a Parabola
- The Smallest Triangle Containing Two Unit Circles
- Area of a Lissajous Figure
- Another Polygonal Spiral
- What's the Area of the Bishop's Hat?
- What's the Probability that Alice Makes Fewer Tosses than Bob?
- Sum the Series
- Buffon's Bent Needle
- A Weight on a Rope
- Spreading Rumors
- Yet Another Infinite Series
- The Smallest Circle Containing Two Ellipses
- A Tetrahelix (from H.S.M. Coxeter) *
- The Area Common to Two Roses
- Find the Parabola Given Three Tangent Lines
- Again with the Infinite Series?
- Area Equals Arclength
- Buffon's Dartboard
- Light Reflecting in an Ellipse
- Maximize the Tetrahedron's Volume
- Compute the Area of a Triangle from the Area of its Shadows
- An Infinite Series involving the Inverse Tangent
- Find the Volume of the Intersecting Cones
- A Differential Equation
- Find the Volume and Surface Area of this Solid
- A Tribute to Martin Gardner
- Find the Determinant of the Matrix
- How Much Green is There in the Wachovia Logo?
- The Locus of Certain Bitangent Points
- How Tall Can the Stack of Hemispheres Be?
- Evaluate the Integral
- An Infinite Series with Factorials
- Find the Ellipse with Least Area Containing Two Unit Circles, etc.
- A Solid with a Square Shadow, a Circular Shadow, and a Triangular Shadow
- What's the Area the Particle Can Reach? o
- What's the Probability of Forming a Triangle? ×
- Find the Volume of the Great Rhombicuboctahedron
- A Limit Involving Partial Sums of the Exponential Function
- A Generalization of the Hyperbolic Trig Functions
- A Trigonometric Problem
- Find the Polynomial
- Find the Plane Tangent to the Three Paraboloids
- Find the Area of the Hexagon Formed by Side-Trisectors
- If You Divide a Cube into Eight Pieces with Three Perpendicular Planes, How Big Can the Largest Piece Be? *
- Integrating Powers of the Cantor Function
- Three Mutually Perpendicular Lines That Pass Through a Circle
- A Problem from Group Theory *
- Minimize the Sum of the Reciprocals of the Distances Between Four Points on a Sphere o
- Two Infinite Series
- Find the Volume of a Region Near a Cone o
- What's the Expected Length of a Slice of a Rectangle? o
- How Far (on Average) to the Circle's Rim? o
- An Integral Involving the Fractional Part Function
- Find the Area Inside the Curve
- Two Infinite Chains of Circles
- A Limit Involving Two Trigonometric Integrals o
- Minimize the Product of the Lengths of Two Perpendicular Diameters of an Ellipse o
- A Limit Involving the Solution of a Trigonometric Equation o
- A Circle Rolling Down a Ramp o
- Find the Area Inside the Parametrized Curve o
- Find the Volume Inside the Two Ellipsoids o
- What's the Expected Distance Between Two Points on a Sphere? (Putnam)
- Happy New Year, 2008
- A Nested Radical Question o
- Find the Limit of the Recursive Sequence
- Minimize the Length of the Normal to a Paraboloid
- Evaluate the Infinite Divisorial Expression
- What's the Probability that the Product is Greater than the Sum?
- How Many Ways Are There to Visit Every Room? o
- Evaluate the Integral
- Find the Ratio of the Areas (Quadric Curve)
- When Are the Roots All Real?
- A Limit Problem Involving Binomial Coefficients
- Evaluate the Power Series (Putnam)
- Alice and Bob Play a Coin-Tossing Game
- Two Compass and Straightedge Problems Involving an Ellipse
- A Hyperbola Tangent to an Ellipse
- Maximize the Volume Inside the Hemisphere and Outside the Sphere
- What's the Expected Distance Between the Two Points?
- Exploring a Common Error in Calculus
- Fencing in a Pen Next to a Parabolic Lake
- A Surface Integral Over the Unit Sphere
- The Surface Area and Volume of a Certain Solid
- Maximize the Area of a Rectangle Inscribed in an Annulus
- Find the Shortest Path on the Intersection of Three Cylinders
- An Infinite Series Involving Arctangent
- A Grazing Zebra
- An Integral Involving the Fractional Part Function
- The Princess and the Moat
- Polynomials on [0,1] Bounded by 1 and −1
- An Infinite Series Involving the Tangent Function
- The Expected Content of Certain Simplices in Two and Three Dimensional Cubes o
- A Cubic Diophantine Equation
- Find the Limit of the Recursive Sequence
- A Limit Involving Factorials
- An Infinite Product Involving the Tangent Function
- Find the Volume of the Region Bounded by Three Paraboloids
- Minimize the Function
- When Does the Transition from Concave to Convex Occur?
- An Infinite Sum Involving the Nearest Integer Function
- An Integral Involving Logarithms and the Floor and Ceiling Functions
- The Locus of Polygonal Centroids o
- Maximizing Humidifier Efficiency
- An Incorrect Version of the Product Rule for Derivatives
- A Tilted Conical Water Glass
- Buffon's Needle in Three Dimensions o
- An Alternating Infinite Series Involving the Natural Logarithm
- An Integral Involving the Natural Logarithm and the Floor Function
- Maximizing the Area of a Triangle (and a Generalization to Three-Space)
- Find the Area of an Ellipse from Three Cross Sectional Lengths
- Find the Surface Area and Volume of a Reuleaux Tetrahedron
- Quadrisect a 3-4-5 Triangle with Two Perpendicular Lines +
- Three Infinite Alternating Series
- Find the Surface Area and Volume of a Rotated Cardioid +
- Find the Smallest Circle Containing a A Right Triangle and Squares Erected on its Sides o
- What's the Probability Two Points Out of
*n*are within Distance*d*of Each Other? o - A Rod Balanced on a Circular Table o
- Evaluate the Integral o
- Find the Areas of the Pieces of the Logo o
- A Folded Sheet of Paper o
- An Erroneous Version of the Chain Rule o
- An Infinite Series Involving the Product of Two Arithmetic Progressions o
- Evaluate the Limit of a Product o
- Maximize the Ratio of the Volume to the Surface Area o
- An Infinite Series Involving the Greatest Odd Divisor o
- The Area of the Triangle Formed by a Tangent Line to the Curve and the Coordinate Axes is Constant (and Others) o
- A 3D Generalization of Advanced Problem #5 o
- A Common Tangent to an Ellipse and a Circle o
- A Question About the Polygon (resp. Polyhedron) Determined by Random Points on a Circle (Resp. Sphere) o
- An Infinite Series Involving a Recursively Defined Sequence o
- Double and Triple Integrals Involving the Logarithm and Floor Functions o
- Minimize the Length of a Tangent Segment to an Ellipse o
- Minimize the Ratio of the Integrals o
- Find the Distribution of Unit's Digits of 2014^2014 o
- A Bug Walking on the Edges of a Polyhedron o
- The Fraction of Water in a Tilted Glass o
- Find the Probability that a Point in a Triangle Divides it into Three Obtuse Triangles o
- The Probability that Three Points on a Sphere Form an Acute Triangle o
- Find the Probability that the Line Segments Meet o
- What's the Area the Llama Can Graze? o
- What's the Probability of Seeing Exactly One Side of a Regular Tetrahedron? o
- Evaluate the Infinite Product o
- Find the Volumes of the Slabs of the Hypercube o
- Bugs on a Regular Polygon o

Back to the Advanced Problem Page

Back to the Problem Corner

Back to the Math Department Homepage.