Year 2016 - Volume 52
2020 - Present

Thomas Britz

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?

Bernard Kachoyan

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?

Hyung Ju Nam and Kim Christian Jalosjos

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.

Chavdar Lalov

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.

David Angell

Q1500 Obtain the number 1500 by using the operations + , − , × , ÷ 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

David Angell

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

Thomas Britz

We are experiencing the most glorious Golden Age of mathematics ever in history. And yet, mathematics is also at a low.

Peter G. Brown

Pascal’s Triangle arises in a very natural way when we expand the powers of x+1 . In this short article, I want to show you just a small sample of the huge number of remarkable patterns that can be found in this triangle of numbers.

Raghavendra G. Kulkarni

Suppose that a person wants to map a cubic equation in x so that a given one of its roots (i.e. solutions) now lies in the origin (x=0 ). Which mapping function is best suited for this task? Suppose that this person changes their mind and now wants to place the root at x=1 for instance.

Farid Haggar

Generic rules for divisibility by small integers in the decimal system are well known and commonly used due to their simplicity. For instance, a number is divisible by 2 (i.e.

Solutions by Denis Potapov, UNSW Australia.

David Angell

Q1501 Find the sum of the sum of the sum of the digits for the number 20162016. (i.e.

David Angell

Q1491 Find the 400th digit after the decimal point in the expansion of (√20+√15)2016.

Thomas Britz

I am proud to present three excellent articles in this issue: a beautiful survey of how to tile the plane with certain pentagons; a fascinating overview of Fibonacci numbers and how they relate to the golden ratio; and a fun and interesting introduction to cryptarithmetic puzzles. .

Maria Fischer

Mathematicians and non-mathematicians have been concerned with finding pentagonal tilings for almost 100 years, yet tiling the plane with convex pentagons remains the only unsolved problem when it comes to monohedral polygonal tiling of the plane.

Robert Schneider

In this expository paper written to commemorate Fibonacci Day 2016, we discuss famous relations involving the Fibonacci sequence, the golden ratio, continued fractions and nested radicals, and show how these fit into a more general framework stemming from the quadratic formula.

Miklos N. Szilagyi

A cryptarithmetic puzzle is a simple mathematical operation in which letters or other symbols have replaced the digits and we are challenged to find the original numbers.

Miklos N. Szilagyi

Competition Winners - Senior Division Clement Hok Wo Chiu The King's School 1st prize

David Angell

Q1511 In a certain country (see Q1494 and Q1502), between every pair of towns there is a highway going in one direction but not in the other direction.

David Angell

Q1501 Find the sum of the sum of the sum of the digits for the number 20162016.