Volume 51
, Issue 1


Welcome to our first fully online issue of Parabola Incorporating Function.

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.

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. 

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 $T_n$ 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 $2014\times1729$ rectangle. This time, however, the particle is projected at an angle of $30^\circ$ above the horizontal.