Volume 52
, Issue 3

2016

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.

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.

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.

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.

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

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.

Q1501 Find the sum of the sum of the sum of the digits for the number $2016^{2016}$.