We investigate Chomp, a game popular with chocolate lovers, and various other combinatorial games associated with it.

A positive rational is a weird fraction if its value is unchanged by an illegitimate, digit-based reduction. In this article, we prove that each weird fraction is uniquely weird and initiate a discussion of the prevalence of weird fractions.

Given a function defined on a subset of the plane whose partial derivatives never change sign, the signs of the partial derivatives form a two-dimensional pattern. We explore what patterns are possible for various planar domains.

A stochastic matrix is a square matrix with nonnegative entries and row sums 1. The simplest example is a permutation matrix, whose rows permute the rows of an identity matrix. A permutation matrix and its inverse are both stochastic. We prove the converse, that is, if a matrix and its inverse are both stochastic, then it is a permutation matrix.

A pair of 6-sided dice cannot be relabeled to make the sums 2, 3,...., 12 equally likely. It is possible to label seven, 10-sided dice so that the sums 7. 8,..., 70 occur equally often. We investigate such relabelings for "pq"-sided dice, where "p" and "q" are distinct primes, and show that these relabelings usually…

A "k"-out-of-"n" system functions as long as at least "k" of its "n" components remain operational. Assuming that component failure times are independent and identically distributed exponential random variables, we find the distribution of system failure time. After some examples, we find the limiting…

A number of papers find the velocity that minimizes the wetness of a traveler caught in the rain. In this capsule we determine, in addition, the necessary amount of forward bend (slouching) so that the traveler stays as dry as possible.

We count the number of group homomorphisms between any two dihedral groups using elementary group theory only.

We give an elementary solution to the famous Basel Problem, originally solved by Euler in 1735. We square the well-known series for arctan(1) due to Leibniz, and use a surprising relation among the re-arranged terms of this squared series.

Combining D'Alembert's ratio test and Cauchy's condensation test, we present a new ratio test for any positive monotone series.

In the popular television show "Survivor", the winner of a million-dollar prize is determined in a final election, where the votes are read aloud as the winner is announced. We hypothesize that the show's producers purposely alter the order of the ballots in order to build audience suspense. We test our hypothesis using the Poisson binomial…

In 1997, Bailey and Bannister showed that a + b greater than c + h holds for all triangles with [gamma] less than arctan (22/7)where a, b, and c are the sides of the triangle, "h" is the altitude to side "c", and [gamma] is the angle opposite c. In this paper, we show that a + b greater than c + h holds approximately 92% of the time for all…

Most quadratic functions are not even, but every parabola has symmetry with respect to some vertical line. Similarly, every cubic has rotational symmetry with respect to some point, though most cubics are not odd. We show that every polynomial has at most one point of symmetry and give conditions under which the polynomial has rotational or…

Many classical problems in elementary calculus use Euclidean geometry. This article takes such a problem and solves it in hyperbolic and in spherical geometry instead. The solution requires only the ability to compute distances and intersections of points in these geometries. The dramatically different results we obtain illustrate the effect…

Reciprocal triangular numbers have appeared in series since the very first infinite series were summed. Here we attack a number of subseries of the reciprocal triangular numbers by methodically expressing them as integrals.