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In a boarding school there are fifteen schoolgirls who always take their daily walks in rows of threes. How can it be arranged so that each schoolgirl walks in the same row ...

Several prizes are awarded periodically for outstanding mathematical achievement. There is no Nobel Prize in mathematics, and the most prestigious mathematical award is known ...

An obtuse triangle is a triangle in which one of the angles is an obtuse angle. (Obviously, only a single angle in a triangle can be obtuse or it wouldn't be a triangle.) A ...

There are certain optimization problems that become unmanageable using combinatorial methods as the number of objects becomes large. A typical example is the traveling ...

A figurate number Te_n of the form Te_n = sum_(k=1)^(n)T_k (1) = 1/6n(n+1)(n+2) (2) = (n+2; 3), (3) where T_k is the kth triangular number and (n; m) is a binomial ...

Let DeltaABC be a triangle and D a point on the side BC. Let I be the incenter, P the center of the circle tangent to the circumcircle and segments AD and BD, Q the center of ...

The number 24 is equal to 4! (four factorial). A number puzzle asks to construct 24 in as many ways possible using elementary mathematical operations on three copies of the ...

The Abel equation of the first kind is given by y^'=f_0(x)+f_1(x)y+f_2(x)y^2+f_3(x)y^3+... (Murphy 1960, p. 23; Zwillinger 1997, p. 120), and the Abel equation of the second ...

The Riemann's moduli space gives the solution to Riemann's moduli problem, which requires an analytic parameterization of the compact Riemann surfaces in a fixed ...

An Abelian variety which is canonically attached to an algebraic variety which is the solution to a certain universal problem. The Albanese variety is dual to the Picard ...