[I was] Assistant Treasurer of my High School General Organization which had a yearly budget of $25,000 ... My duties included keeping books ... making monthly and quarterly reports and reconciling bank statements.

When I was at CALTEC I went there thinking I wanted to be a civil engineer and then I thought I wanted to be an organic chemist - I loved all those formulae for organic molecules.

I feel that I am the best qualified candidate for the office of ASCIT Treasurer. As experience I cite the following: Assistant Treasurer of my High School General Organization which had a yearly budget of $25,000, approximately twice that of ASCIT. My duties included keeping books, in a manner similar to those of ASCIT, making monthly and quarterly reports and reconciling bank statements. "Capitalist" of Ricketts House, involving businesses grossing $2,500 yearly, considerably more than a class budget. I feel that I have had probably more experience than any student in the handling of money matters on a large scale.

... quite a provincial place, in Pasadena which is archetypal provincial America.

I found Berkeley much more interesting as you could imagine - this was 1960 and there was lots going on. And then I got married and I had an apartment just off Telegraph Avenue.

I thought, why have they been hiding these from us - they should be teaching this in High School.

Some time ago, the following problem occurred to me: which fits better, a round peg in a square hole or a square peg in a round hole? This can easily be solved once one arrives at the following mathematical formulation of the problem. Which is larger: the ratio of the area of a circle to the area of the circumscribed square or the ratio of the area of a square to the area of the circumscribed circle? One easily finds that the first ratio is $\large\frac{\pi}{4}\normalsize$ and that the second is $\large\frac{2}{\pi}\normalsize$. Since the first is larger, we may conclude that a round peg fits better in a square hole than a square peg fits in a round hole. More recently, it occurred to me that the above question could be easily generalised to n dimensions. The remainder of this paper will be devoted to the following

Theorem. The n-ball fits better in the n-cube than the n-cube fits in the n-ball if
and only if n ≤ 8.

The first author [David Singmaster] was an NSF Graduate Fellow at the University of California at the time of writing this paper.

... in 1971 [the team] continued their systematic survey across the area. During a line survey on August 7th the team photographer, David Singmaster, went a little off course to retrieve a stray marker, and that's when he discovered a bizarre, recently exposed timber poking out of the sand. Honor went over to investigate ... [Singmaster] had found what [the team] later determined to be the sternpost of the vessel, recently exposed by the shifting sands, in just 2.5 metres of water.

In the January, 1973, issue of this magazine, Richard Gibbs has restated the well-known fact that a 2m × 2m chessboard, with two diagonally opposite corners deleted, cannot be covered by dominoes since the deleted squares are of the same colour. He then asked:

(a) Can a 2m × 2m board be covered with dominoes if we remove any two squares of opposite colour?

(b) Can a (2m + 1) × (2m + 1) board be covered if we remove any square of the major (or corner) colour?

It is well known and easily seen that an m × n rectangle can be covered with dominoes if and only if m or n is even. This led me to consider Gibbs' problem (a) for m × 2n boards and thence to consider his problem (b) for (2m + 1) × (2n + 1) boards. Theorems 1 and 3 below answer these generalised problems affirmatively, except for the case when m = 1 in (a), in which case a further necessary and sufficient condition for covering is given as Theorem 2.

It is not difficult to see that (a) fails if we delete four squares, but I was rather delighted to find that (b) is also true if we remove any three squares, two of the major colour and one of the minor, provided m ≠ 0 and n ≠ 0. This is proven as Theorem 4. The extension of (b) to five squares fails.

My wife and I spent a year in Italy, a country that we both love. In Italy there is a law that requires banks to spend 2% of their profits on 'good works', which can be interpreted as publishing facsimiles of medieval manuscripts on mathematics. A few years before we arrived in Tuscany, the Cassa di Risparmio di Firenze published a facsimile of the magnificent illuminated manuscript of Filippo Calandri's 'Trattato di Arithmetica', Florence, 1491. The manuscript is one of the treasures of the Biblioteca Riccardiana in Florence. It contains 230 miniatures in gold and silver, some attributed to the workshop of Botticelli, and many depicting recreational problems set against Italian cityscapes. The manuscript was commissioned by Lorenzo the Magnificent for the education of his son, Giuliano de' Medici, the future Pope Leo X. When Italian banks sponsor facsimiles and reprints, they tend to do so in limited numbers for presentation to visiting dignitaries and business associates. It took me thirty years to find my own copy of the Calandri facsimile, which finally turned up in a Florentine bookseller's catalogue.

Penrose did not believe anyone could do it without consulting a pocket full of notes and his coat pocket was full of envelopes with move diagrams written on them. He was amazed to discover that Conway could do it from memory - it only took him about $3\large\frac{1}{2}\normalsize$ minutes. Everybody thought this was mind-boggling. Conway gave me suggestions how you could study certain bits - ways you could study part of the structure of the cube - when I had managed to get a cube from one of the Hungarians. The Hungarians had discovered there were no customs regulations on cubes - they could bring them out and use them as worth more than hard currency. They could take Rubik Cubes abroad and trade them for books, even lodgings, etc. After about two weeks I had worked out a method of solving it.

The last few months have been very hectic as David Singmaster Ltd. has gotten launched. We had a stand at the London Toy Fair, I went to the Nuremberg Toy Fair and Jane Nankivell went to the Paris Toy Fair. I counted about 50 new puzzles which will appear this year: A report on some of these will occupy most of this issue. There are many other new products which will have to wait for the next Circular. ... We are developing a great range of contacts in the puzzle industry and have begun to act as agents or manufacturers for several inventors. We can either arrange to manufacture on a small scale or pass on ideas to major producers such as Mèffert or Pentangle. At the moment, this is a new area of the business and we are feeling our way ...

Unfortunately I had a massive overdose of cubism in 1982-83. David Singmaster Ltd. was closed down, and I lost a fair amount of money - more than I had made previously. This led to prolonged tax negotiations. ... I was teaching several extra courses in 1983-84, including the geometry course which was being taught for the first time. I also spent a lot of time helping to rewrite a Department submission that had been rejected. I have also started on some other projects which have taken up much of my time. ... Fortunately, I was promoted to a Readership (= Research Professorship), the first in my Faculty, as of September 1984 and this is giving me more time to get caught up. ... In a week, I am going to City College of New York for the Autumn term [of 1985].

In November 1981, I was on a 45 minute BBC TV show called 'The Adventure Game'. This was a series in which three hapless members of the public are recruited to go to a mythical planet where the inhabitants enjoy playing tricks on visitors. ... Some of the tricks are straightforward - when you turned on the water in the kitchen, the radio came on, so you tried turning on the radio to get water. There is a mole type who tries to mislead us - she asked me to open a wine bottle and gave me a corkscrew. I looked at it and responded: "Ah, a left-handed corkscrew. I've just bought a bunch of these," and proceeded to open the wine. They cut this part out! Anyway, it was good fun trying to solve problems, but it goes so fast that one doesn't even see all the clues.

In June 1998 to November 1999, I was a frequent panellist on 'Puzzle Panel', a BBC Radio Two half-hour programme. The chairman was Chris Maslanka and there would be three others selected from perhaps a dozen people that were used, mostly people with some puzzling connection who were puzzle contributors to various newspapers and magazines. We would each come with about two suitable puzzles which would be put to the panel. Chris would set a problem for the listeners and after the first programme, we would get solutions and further problems sent in by listeners. Unfortunately it was never put on at a good time. We enjoyed doing the programmes and got a respectable audience, but I think the BBC authorities couldn't understand what was going on!

For some years I have been collecting information about where mathematicians were born, lived, worked, died, or are buried or commemorated.

I've taken early retirement in order to work on several books I am compiling: Sources in Recreational Mathematics; A Mathematical Gazetteer; Notes on the History of Science and Technology in London. I collect books on these fields and on cartoons, humour, and language. I spend a lot of time in libraries and bookshops and I deal in books on recreational mathematics. We go to theatre, art galleries, etc. and visit friends and be tourists.

I was one of the contributors to 'A Lifetime of Puzzles', a festschrift for Martin Gardner, published in 2008. My subject was the first recreational mathematics book, written by Luca Pacioli, the friend and collaborator of Leonardo Da Vinci. 'De Viribus Quantitatis' (On the Powers of Numbers) is regarded as the foundation of modern magic and numerical puzzles, and is believed to be the first documentation of magic tricks with cards and coins. There is quite an overlap between people who are interested in the history of magic, and those who specialise in recreational mathematics. Pacioli's book is an early example of this overlapping interest, which can be found in many later books on puzzles, particularly if the magic depends on binary arithmetic.

David was an extremely nice and generous person, a large, friendly, smiley figure, with a great capacity to think and play mathematically. He was one of a kind and will be sorely missed by all who knew him.

David had a delight and a passion for sharing. A visit to his house was an adventure, and once you were there it was extraordinarily difficult to leave! It was packed, floor to ceiling, with books, puzzles, and games. 'Just one more thing' was his catchphrase, as he would first show, then watch you struggle with, then himself struggle in turn to remember how to solve a mechanical puzzle of one sort or another. His tongue would poke out, first on one side, then the other, then back again, as all the while he talked about the history of the item, and how it had come into his possession. He delighted in the struggle, and each time he succeeded in solving a puzzle again his joy was evident, and you were invited to share it with him.