Welcome to our first fully online issue of Parabola Incorporating Function.
Catherine Greenhill
It's not every day that a mathematics puzzle makes it into mainstream media. But that's what happened recently with "Cheryl's Birthday problem". This problem was posted by Kenneth Kong, the host of a Singaporean TV show, on his Facebook page on 10 April, and it went viral.
David Treeby and Jenny Tang
Finding two ways to enumerate the same collection of objects can often give rise to useful formulae. For instance, the sum \(1+2+\cdots+n\) can be interpreted as the maximum number of different handshakes between \(n+1\) people.
Anand Prakash
Polygonal numbers enumerate the number of points in a regular geometrical arrangement of the points in the shape of a regular polygon. An example is the triangular number Tn which enumerates the number of points in a regular triangular lattice of points whose overall shape is a triangle.
Parabola incorporating Function would like to thank Sin Keong Tong for contributing Problem 1472.
Q1461 As in Problems 1442 and 1452, a particle is projected from one corner of a rectangle. This time, however, the particle is projected at an angle of above the horizontal.
Bruce Henry and Thomas Britz
Dear Readers, this is my last message to you as Editor of Parabola.
Christopher K. Winkler
When learning the intuition behind definite integration, calculus students often learn how to find the area under a curve by using a Riemann sum.
Bernard Kachoyan
Ever thought of batting in cricket as a life and death struggle against hostile forces? It always seemed that way when I batted anyway.
Well you might be more accurate than you think in looking at it that way.
Farid Haggar
An enclosure of length unit is constructed around two adjoining walls of unlimited length. It is made of straight sections, referred to as an -enclosure , designed so as to maximise the enclosed area , where is the angle formed by the walls.
Competition Winners - Senior Division
Seyoon Ragavan Knox Grammar School 1st prize
Competition Winners - Junior Division
Richard Gong Sydney Grammar School 1st prize
Junior Division - Problems and Solutions
Solutions by Denis Potapov
David Angell
Q1481 Prove that if the denominator \(q\) of a fraction \(p/q\) is the number consisting of \(n\), all equal to \(99\), and if \(p\) is less than \(g\), then \(p/q\) can be written as a repeating decimal in which the repeating part has length \(n\) and contains the digits of \(p\), preceded by a sufficient number of \(0\)s to give that length.
David Angell
Q1471 Find the positive integer which has 77 proper divisors, with the sum of the proper divisors being 673673. (Proper divisors are all divisors except the number itself: for example, the proper divisors of 2020 are 1, 2, 4, 5, 101).