What sentence in this Mathematical Gazette contains seven a’s, four c’s, thirty-two e’s, eight f’s, five g’s, ten h’s, twelve i’s, three l’s, three m’s, fifteen n’s, eight o’s, one q, seven r’s, twenty-seven s’s, twenty-five t’s, four u’s, eight v’s, seven w’s, four y’s & two z’s?

I have considered elsewhere the modelling of the pricing policies of Electricity Boards, Gas Boards and British Telecom [1]. In this article the combined effect of the standing charge rebate and estimate accounts are considered and two results contrary to popular belief are shown.

Many people have had the experience of borrowing a sum of money which is to be repaid with interest by making equal monthly payments over a year or a number of years. Two problems suggest themselves:

1. If the annual rate of interest is known what is the value of each monthly payment?

2. If the monthly payment is known, what is the annual rate of interest?

Oxbridge Tripos examination questions originating from the turn of the century have had a marked effect on the teaching of mechanics both at School and at University. These questions, reproduced in the standard textbooks of the day, were the stable diet of the undergraduate population over so many years and set the pattern for a style of question in which the student applies mechanical principles by rote without ever questioning the validity or relevance of those principles. An unfortunate consequence of this state of affairs is that mechanics has been largely overlooked as a vehicle for the teaching of mathematical modelling. There have been moves recently to make questions more “relevant” and it is not unknown to see illustrations of “real” boats, shotputters etc. However, the student is still expected to answer the question “mechanically”, if the reader will excuse the pun, without any discussion of the modelling process. How refreshing it is, even with first year undergraduates, to look at the problem of a tin can being knocked off a wall by a bullet and, instead of asking the students to apply two conservation laws in order to determine the speed with which the can hits the ground, to ask under what assumptions the two conservation laws would appropriately model the physical situation? It is quite staggering how the lecture theatre erupts with ideas, suggestions and interest.

The aim of this short article is to produce a sequence of real numbers x1, x2, x3, … with the property that, for each n,

x1 + x2 + … + xn = x1x2 = xn.

This turns out to be an interesting classroom exercise involving simple equations and iteration.

This article begins with the consideration of a short program designed to produce random values from a normal distribution and goes on to suggest how a similar program might be used to introduce confidence intervals to a group of A-level students. The programs are written in BASIC for the BBC microcomputer.

This article describes a new and general line-and-conic property, leading to a consideration of a ‘six-point’ circle and the related geometry of an interesting visual illusion.