Solution: line dividing a triangle
We publish here the solution to the divertimento Line dividing a triangle. The fun: Those of us who thought of including in our blog a section in which to pose problems for the entertainment of […]
solutions
Solution: The rigged scale
We publish here the solution to the divertimento The rigged scale. The fun: A trader sells rice using a scale with one arm longer than the other and a single 1 kg weight. In order […]
Solution: Interfaculty championship
We publish the solution to the divertimento Interfaculty Championship. The fun: Three faculties, Mathematics, Physics and Chemistry, participated in a university sports championship. Each had one participant in each event. Isabel, a student from the […]
Solution: a problem of ages
We publish here the solution to the divertimento A problem of ages. The divertimento: After some time without seeing each other, Alberto and Manolo meet in the street and talk about their ages. “When you […]
Solution: Summer probabilities
We publish here the solution to the summer probabilities divertimento. The fun: Anna and Beatrice are playing a heads or tails coin game, tossing alternately. When Anne has tossed for the \((n+1)\)-th time, they have to […]
Solution: Numbered houses
Here is the solution to the numbered houses divertimento. The fun The conversation between two mathematicians exchanging home addresses goes as follows: –What is the number of your house? –In my street the houses are numbered […]
Solution: Trapezoids
This is the solution to the Trapezoids divertimento. The fun Given two positive integers \(a\) and \(b\), the relations existing between their different Pythagorean means (arithmetic, geometric and harmonic) and their quadratic mean are well known, […]
Solution: Four chess pieces
We publish here the solution to the four chess pieces divertimento. The fun A chessboard has size \(n \times n\), with \(n >1\). What is the smallest number of pieces to place on the board to […]
Solution: playing with triangles
We are publishing here the solution to the divertimento Playing with triangles. The fun A figure consisting of an equilateral triangle and a line parallel to one side passing through its centre is given. A […]
Solution: single-dose tablets
This is the solution to the divertimento Single-dose tablets. The fun A bottle contains 50 single-dose tablets of a medicine and 50 double-dose tablets. On arrival, each patient randomly takes out a pill; if it […]