Volume 52
, Issue 1

2016

On 9 January 2016, Professor Peter Gavin Hall died, bringing great sadness to the mathematical community. For aside from his profound academic talent and contributions, he is remembered and missed for his immense and yet gentle generosity. Why is it that mathematics seems to attract kind and generous leaders?

Let us suppose that you are looking for some objects in a particular area. Now also suppose that you ﬁnd nothing after searching the area. Is there really nothing there? Or, more generally, if you ﬁnd N objects, then how many objects are there left to be found?

This paper shows the construction of linkages that draw parts of three well-known curves characterized by distances from points and lines: the lemniscate of Bernoulli, the Peaucellier-Lipkin linkage for a straight line, and Yates’ parabola.

You have a 3L jug and a 5L jug. Each is empty but you have tap of running water that you can use to fill each jug. Can you fill the big jug with 4L water by filling, emptying and pouring water from one jug to the other? This article shows how you can solve these type of problems in general.

Q1500 Obtain the number $1500$ by using the operations $+$, $-$, $\times$, $\div$ on the numbers $1,2,3,4,5,6,7,8,9$, in that order.  Brackets are allowed, but you cannot join digits to form multi--digit numbers: for example, you may not write 1 next to 2 and call this 12.  One possibility

Q1481 Prove that if the denominator $q$ of a fraction $p/q$ is the number consisting of $n$ digits, all equal to $9$, and if $p$ is less than $q$, 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 numb