Ebook: Mathematical morsels

The chess tournament -- The ordered partitions of n -- Regions in a circle -- The ferry boats -- The bulging semicircle -- The chauffeur problem -- The screens in the corner -- Coloring the plane -- An obvious maximum -- cos 17x=f(cos x) -- A square in a lattice -- An opaque square -- x's and o's -- A surprising property of right-angled triangles -- The digits of 4444⁴⁴⁴⁴ -- [Sigma](n)+[Phi](n)=n·d(n) -- On k-clouds -- A minimal sum -- The last three digits of 7⁹⁹⁹⁹ -- Rolling a die -- Piercing a cube -- Double sequences -- Point-splitting circles -- On the lengths of the sides of a triangle -- No calculus please -- a[superscript b] and b[superscript a] -- A mathematical joke -- Maps on a sphere -- Convex regions in the plane -- Simultaneous Diophantine equations -- A reflected tangent -- The elegantly destroyed checkerboard -- The snowballs -- Writing the numbers from one to a billion -- Abutting, nonoverlapping unit squares -- A Diophantine equation -- The Fibonacci sequence -- An Erdös inequality -- Sharing lattice points -- Perfect numbers -- The sides of a quadrilateral -- Primes in arithmetic progression -- On Cevians -- The cows and the sheep -- A sequence of squares -- The inscribed decagon -- Red and blue dots -- Swale's method -- On [pi constant](n) -- A constant chord -- The number of inner diagonals -- Loading the dice -- A curious sequence -- Long strings of consecutive natural numbers -- A minimal inscribed quadrilateral -- Triangular numbers -- On a regular n-gon -- The Fermat numbers -- An inequality of reciprocals -- The perfect 4th power -- Packing squares -- Red and green balls -- Composite terms in arithmetic progression -- Abutting equilateral triangles -- The tests -- An application of Ptolemy's theorem -- Another Diophantine equation -- An unusual property of complex numbers -- A chain of circles -- Repeated digits at the end of a square -- An angle bisector -- A system of inequalities -- An unexpected property of a regular 26-gon -- More on perfect squares -- An unusual polynomial -- Cyclic centroids -- An easy remainder -- A curious property of 3 -- A square within a square -- Always a square -- Grouping the natural numbers -- Triangles with sides in arithmetic progression -- Fractions by permutation -- On binomial coefficients -- The Fermat number F₇₃ -- A cyclic quadrilateral -- Special triples of natural numbers -- The sums of the primes -- Another curious sequence -- The ellipse and the lattice -- Archimedes triangles