Best of the MathNerds

Precalculus and other Elementary Math

• The Case of the Missing Mangos Fractional ownership in a mango cooperative.

• Buildings and Ladders How high do the ladders reach? An exercise from the Field Team.

• Factor This Factor the expression A^3(B-C) + B^3(C-A) + C^3(A-B).

• Digit Reversal Solve the equation 4(ABCDE) = EDCBA.

• Rock Star Shuffle Get the band U2 across the bridge in 17 minutes.

• The Buckled Rail Who would notice a error of one foot in a mile-long rail?

• McNuggets Building your McNugget collection.

Number Theory

• An Excess of Divisors Why are there more divisors ending in 1 or 9 than in 3 or 7?

• Pell Mell We're looking for a few good square roots.

• The Magnificent Seven Writing 1 as a sum of seven reciprocals.

• Irrational Exuberance Is the sum of this infinite series irrational?

• Non-Dividing Sets What's the biggest subset such that no integer divides any other?

Discrete Math

• The Counterfeit Penny Find the counterfeit using a balance scale.

• The Twelve Coins (or Twelve Bags of Gold) Find the false coin in three weighings of a balance scale, when you don't know whether the false coin is heavy or light.

• Drawing the Line Given a finite set of points in the plane, is there a line intersecting exactly two of them?

• Crazy Dice Our Crazy Dice work just as well as old boring regular dice and are more fun.

• Chipping N Stacking poker chips for fun and profit.

Calculus

• The Mirror Trick How to maximize cross-sections without calculus.

• The Hole Problem A napkin-ring invariant.

• The Integral Challenge Evaluate an integral without integrating.

Mathematical Analysis

• The First Digit of 2^n Which digit occurs most frequently?

• The Notorious Jumping Function of Continuum County How discontinuous can a monotonic function be?

Topology, Set Theory, Optimization, and other Advanced Math

• Mazurkiewicz's Theorem on 2-Sets Can you construct a set of points in the plane such that every line of the plane intersects the set in exactly two points?

• The Nasties of the Round Table Math as a corporate survival strategy.

• The Shortest Road Network Building the shortest road connecting four towns.