To live to a ripe old age, untroubled by health problems, physical or mental, is an almost universal aspiration. But most people are not so lucky and will likely be in care homes for their final years, with varying levels of disease, disability and dementia. Kinley et al [1] maintain that over a fifth of the population of developed countries die in care homes. Moreover, the financial cost of this end of life care, which is the focus of this paper, can be daunting and require much planning [2]. It was reported in 2017 that, in the UK, care home costs are rising up to twice as fast as inflation [3]. Consequently the question arises about the long term affordability of such care to those having to fund it, a question that ever more people both nationally and globally are having to confront.

E. H. Neville was Librarian of the Mathematical Association for over thirty years, from 1923 to 1954.For more than half of that time Neville was not only Librarian but custodian of the books which were handsomely shelved and displayed in his own home, first in his house on Castle Hill, Reading, and then in his first house in Sonning.

My younger son has become interested in the game “dungeons and dragons”. He is intrigued by the shapes of the dice that are used to play the game and by the number of faces they have. Besides the standard cubical die with its 6 faces, there are the other regular solids with 4,8,12 and 20 faces. There is also a die with 10 faces, each in the form of a kite, and my informant points out longingly that our local games shop has a die with 100 faces. “Could you have one with an odd number of faces?” he asks.

His innocent question led me to think about many mathematical aspects of dice. This article answers his question, examines the geometry of dice (highlighting some unnamed solids which deserve to be better known to model-makers), considers surprising aspects of the mechanics of tossing dice and describes sets of unusual dice whose probabilities offer scope for many games which can trap the unwary gambler.

There are two forms of setting out questions involving the reduction of shillings to £'s. They are:

In example (i), after crossing off the nought of the 20 and the last figure of the dividend, division is by 2 ; whilst in example (ii) division is by 20. Consequently, in (ii), the first figure of the quotient is one place further to the right than it is in (i). The divisor, 20, is often omitted in both examples.