Computing, Information Systems and Mathematics 87 Rodenhurst Road South Bank University London, SW4 8AF, England London, SE1 0AA, England Tel/fax: 0181-674 3676 Tel: 0171-815 7411 Fax: 0171-815 7499 E-mail: ZINGMAST@VAX.SBU.AC.UK

PUBLICATIONS of David Singmaster

Last amended on 4 agosto 1996. 1964. On round pegs in square holes and square pegs in round holes. Math. Mag. 37:5 (Nov 1964) 335-337. 1966. A maximal generalization of Fermat's theorem. Math. Mag. 39:2 (3/1966) 103-107. 1967. Forbidden regions are convex. Amer. Math. Monthly 74:2 (Feb 1967) 184- 186. Jointly with G. Singmaster. 1970. Some counterexamples and problems on linear recurrence relations. Fibonacci Quarterly 8:3 (Apr 1970) 264-267 & 279. 1971. On the concept of directed distance. L'Enseignement Math‚matique 17:1 (Jan/Apr 1971) 87-91. How often does an integer occur as a binomial coefficient? Amer. Math. Monthly 78:4 (Apr 1971) 385-386. 1972. The eigenvalues of the n-dimensional octahedron. Notices Amer. Math. Soc. 19:6 (Oct 1972) A-684, #72T-A243. The eigenvalues of the icosahedron and dodecahedron. Notices Amer. Math. Soc. 19:7 (Nov 1972) A-750, #72T-A269. 1973. Some corrections to Carlson's 'Determination of Heronian triangles'. Fibonacci Quarterly 11:2 (Apr 1973) 157-158. The rings of order p2 - A remark on a paper of Heuer. Content used in: Notes & Comments; Math. Mag. 46:3 (May 1973) 160-161. Notes on binomial coefficients. IV - Proof of a conjecture of Gould on the GCD's of two triples of binomial coefficients. Fibonacci Quarterly 11:3 (Oct 1973) 282-284. Hamiltonian circuits on the regular polyhedra. Notices Amer. Math. Soc. 20:5 (Aug 1973) A-476, #73T-A199. 1974. On polynomial functions (mod m). J. Number Theory 6:5 (Oct 1974) 345- 352. Notes on binomial coefficients. I - A generalization of Lucas' congruence. J. London Math. Soc. (2) 8:3 (Aug 1974) 545-548. Notes on binomial coefficients. II - The least n such that pe divides an r-nomial coefficient of rank n. J. London Math. Soc. (2) 8:3 (Aug 1974) 549-554. Notes on binomial coefficients. III - Any integer divides almost all binomial coefficients. J. London Math. Soc. (2) 8:3 (Aug 1974) 555-560. Contributions to Open Questions in Mathematics. Ed. by Dagmar R. Henney. George Washington Univ., Washington, DC, 1974. Pp. 50-51 & 63-69. 1975. Repeated binomial coefficients and Fibonacci numbers. Fibonacci Quarterly 13:4 (Dec 1975) 295-298. Covering deleted chessboards with dominoes. Math. Mag. 48:2 (Mar 1975) 59-66. Hamiltonian circuits on the n-dimensional octahedron. J. Combinatorial Theory Ser. B 19:1 (Aug 1975) 1-4. Enumerating unlabelled Hamiltonian circuits. In: Vortragsauszge der Tagung ber numerische Methoden .... Internat. Series Numer. Math 29 (1975) 117-130. 1976. Genera of the London Underground and Paris Metro. Manifold 18 (Spring 1976) 15-19. (Abstract appeared in: Graph Theory Newsletter 3:5 (May 1974) 3, #8.) Some classes of Hamiltonian 3-polytopes. Proc. Fifth British Comb. Conf., 1975. Congressus Numerantium 15 (1976) 551-558. Jointly with Anthony Hill. Labelled and unlabelled Hamiltonian circuits in a class of 3-polytopes. Proc. Fifth British Comb. Conf., 1975. Congressus Numerantium 15 (1976) 293-305. Jointly with Anthony Hill. 1977. The Art of Debugging. Polytechnic of the South Bank Computer Centre, London, Apr 1977, 10pp. List of 16mm Films on Mathematical Subjects at Tertiary Level. Published for the London Mathematical Society film meeting, Oct 1977, 10pp. Another Clapham scientist. Occasional Sheet of the Clapham Antiquarian Society, No. 347 (Feb 1977). [About Kekul‚.] 1978. On the asymptotic behavior of S (n+t)axn as x ð 1. Indian J. Math. 19:3 (1977 (1978)) 163-166. (Abstract appeared as: Notices Amer. Math. Soc. 18:2 (Feb 1971) 407, #71T-B32.) On the relationships among the axioms for a metric space and for general axiomatic systems. Port. Math. 37:1-2 (1978) 145-155. Jointly with D. J. Souppouris. A constrained isoperimetric problem. Math. Proc. Cambridge Philos. Soc. 83 (1978) 73-82. Jointly with D. J. Souppouris. An elementary evaluation of the Catalan numbers. Amer. Math. Monthly 85:5 (May 1978) 366-368. Hamiltonian circuits on some special graphs. Notices Amer. Math. Soc. 25:5 (Aug 1978) A-481/482, #78T-A141. Getting Started on Mathematical Research. Computer file GETSTA.TXT, revised numerous times. Presently 13pp. An unusual Polytechnic contribution to mathematics. Excerpts used: South Bank Diary 1978/79 No. 4 (9 Nov 1978) 1. Revised, 4pp, 1992 1979. Some Catalan correspondences. J. London Math. Soc. (2) 19 (1979) 203- 206. Letter to the Editor: History of Heronian triangles. Math. Spectrum 11:2 (1978/79) 58-59. List of 16mm Films on Mathematical Subjects. 1st ed. Open University, Milton Keynes, May 1979, 22pp. 2nd ed. " " Oct 1979, 23pp. 3rd ed. Polytechnic of the South Bank, London, Mar 1980, 23pp. 4th ed. " " Jul 1982, 33pp. 5th ed. " " Oct 1983, 36pp. Six-sided magic. The Observer (17 Jun 1979) 40. Letter to the Editor: Cube puzzle. Historia Math. 6:2 (May 1979) 194. [On Instant Insanity.] 1979 - continued. The Hungarian Magic Cube. Math. Intell. 2:1 (1979) 29-30 (+ Cover & p. 1). Czech translation by Old_ich Kowalski. Ma_arsk  kouzeln  kostka. Pokroky Mat. Fyz. Astronom. (2) 26 (1981) 86-88. Notes on the 'Magic Cube'. Published by myself. MS, 40pp, 23 Feb 1979. 1st ed., Typed, with supplement and first addendum, 30 pp, 2 Oct 1979. 2nd ed., 31 pp, 22 Oct 1979. 3rd ed., 34 pp, 30 Nov 1979. 4th ed., 36 pp, 16 Jan 1980. 5th ed., retitled: Notes on Rubik's 'Magic Cube', 75pp, 6 Aug 1980. US edition by Enslow Publishers, Hillside, NJ, 1981 Penguin edition, Sep 1981. Dutch translation by Ronald Jonkers & Paul Joorman. Kanttekeningen bij de Kubus van Rubik. Bert Bakker, Utrecht, 1981. 128pp. Spanish translation by Gilbert V. Torbeck. Notas sobre el cubo de Rubik. Altalena Editores, Madrid, 1981. 139pp. Letter to the Editor: The circle and the golden pyramid. Math. Gaz. 63 (No. 426) (Dec 1979) 271. 1980. Divisibility of binomial and multinomial coefficients by primes and prime powers. In: A Collection of Manuscripts Related to the Fibonacci Sequence. Ed. by V. E. Hoggatt Jr. & M. Bicknell-Johnson. The Fibonacci Association, 1980, pp. 98-113. Arranging a dartboard. Bull. Inst. Math. Appl. 16:4 (Apr 1980) 93-97. The Magic Cube. Games & Puzzles 76 (Spring 1980) 4-6. Letter to the Editor: The problem of square pegs and round holes. ILEA Contact 9:13 (12 Sep 1980) 12. Golfballs. M500 62 (Jan/Feb 1980) 4-5. 1981. The number of representations of one as a sum of unit fractions. Used in: R. K. Guy; Unsolved Problems in Number Theory; Springer, NY, 1981; Prob. D11, p. 89. Almost all games are first person games. Eureka 41 (1981) 33-37. A new paradox? Math. Spectrum 13:3 (1980/81) 76 & 83. The last non-zero digit of n! - a new random number generator. Abstracts Amer. Math. Soc. 2:1 (Jan 1981) 237, #81T-A14. Theoretical probabilities for a cuboidal die. Math. Gaz. 65 (No. 433) (Oct 1981) 208-210. The incredible cube. Games & Puzzles 81 (Summer 1981) 4, 5, 10. Membership List of the London Mathematical Society - 1 October 1980. General editing and composition of textual material, e.g. history of the Society. London Math. Soc., 1981, 71pp. Cube news again. Math. Intell. 3:3 (1981) 107-108. The British Mathematical Colloquium. Math. Intell. 3:4 (1981) 165. The fascination of Rubik's Cube. Hungarian translation: A Rubik-kocka ig‚zete El”sz¢. In: E. Rubik, et al.; A B_v”s Kocka; M_szaki K”nyvkiad¢, Budapest, 1981, pp. 7-12. Bulgarian translation: aa a P . In: Epo P, et al.; aec , Tekhnika, Sofia, 1983, pp. 7-11. MŠffert's Pyraminx. Foreword to: Ronald F. Turner-Smith; The Amazing Pyraminx. MŠffert Novelties, Hong Kong, 1981, pp. 9-10. Rubik's Cube and other ways to cure sanity. ILEA Contact (16 Oct 1981) 5. Society's Needs, High Technology Teaching Aids and the Undergraduate Mathematics Curriculum. Proceedings of the University Mathematics Teaching Conference, 1980. (General editor and author of some sections.) Shell Centre for Mathematical Education, Univ. of Nottingham, 1981. Formulae for cubic content. Sunday Times (29 Nov 1981) 36. Correction (20 Dec 1981) 27. Colours. M500 75 (Dec 1981) 9. Translation editor of: Tom Werneck; Mastering the Magic Pyramid; Evans Brothers, London, 1981, 112pp. 1982. Rubik's Cube - MŠffert's Pyraminx. Content used as the basis of: Trevor Truran; All better and twisted; Top Puzzles, No. 4 (Dec 81/Jan 82) 26-27. Sums of squares and pyramidal numbers. Math. Gaz. 66 (No. 436) (Jun 1982) 100-104. Handbook of Cubik Math. Enslow Publishers, Hillside, NJ, 1982, 194pp. Jointly with A. H. Frey, Jr. Rubik's Cube and other puzzling phenomena. Chelwood Review 12 (Jun 1982) 24-27. A "Putney" mathematician - Srinivasa Ramanujan. Wandsworth Historian 33 (Jun 1982) 2. Even more cube rolling. M500 79 (Jun 1982) 6-7. Pluperfect numbers. M500 79 (Jun 1982) 12. Moral and mathematical lessons from a Rubik Cube. New Scientist 96 (No. 1337/1338) (23/30 Dec 1982) 786-791. Almost all partizan games are first person and almost all impartial games are maximal. J. Combin. Inform. System Sci. 7:4 (1982) 270-274. 1983. The educational value of the Hungarian Magic Cube. In: Proceedings of the Fourth International Congress on Mathematical Education.. Birkh„user, Boston, 1983, pp. 307-312. [An expanded version was distributed at the BAAS meeting at York, Sep 1981.] Some Lucas pseudo-primes. Abstracts Amer. Math. Soc. 4:2 (Feb 1983) 197, #83T-10-146. Letter - comment on Note 66.35: The construction of an approximately regular n-gon. Math. Gaz. 67 (No. 440) (Jun 1983) 142. More Moser configurations. M500 83 (Apr 1983) 5. Queries and problems on sources in recreational mathematics. M500 83 (Apr 1983) 8-13. 1984. An elementary number theory result. Irish Math. Soc. Newsletter 12 (Dec 1984) 10-13. Jointly with P. J. Birch. Hungarian Rings groups. Bull. Inst. Math. Appl. 20:9/10 (Sep/Oct 1984) 137-139. More on Graham's discs. M500 86 (Feb 1984) 2-3. Divisive difficulties - problem proposal and solution. Nature 310 (No. 5977) (9 Aug 1984) 521 & (No. 5979) (23 Aug 1984) 710. 1985. Puzzles from the Greek Anthology. Math. Spectrum 17:1 (1984/85) 11-15. The legal values of pi. Math. Intell. 7:2 (1985) 69-72. Remarks on 'An elementary number theory result'. Irish Math. Soc. Newsletter 14 (Sep 1985) 31-32. Sources in recreational mathematics. Crux Math. 11:5 (May 1985) 145. Department Research Report 1981-1984. 20pp, Summer 1985. Faculty Research Register 1984-85. 27pp, Summer 1985. [Keplerian pattern.] London Math. Soc. Newsletter 122 (Oct 1985) 12. Letter: Recreational mathematics sources. Math. Mag. 58:5 (Nov 1985) 308. Comment on the history of Heronian triangles. Crux Math. 11:7 (Sep 1985) 222-223. 1986. Department Research Report 1981-1985. 33pp, Oct 1986. The nets of the regular polyhedra. In: Notes from New York Graph Theory Day X, 23 Nov 1985. Ed. by J. W. Kennedy & L. V. Quintas. New York Acad. Sci., 1986, p. 26. Jointly with Peter Light. Sources in recreational mathematics. Ibid., p. 27. How many Eulerian circuits are there in a complete graph? Ibid., p. 28. Keplerian pattern. London Math. Soc. Newsletter 130 (Jun 1986) 2. 1986 - continued. Sources in Recreational Mathematics and Queries and Problems in the History of Recreational Mathematics. First preliminary edition for the Strens Memorial Conference, Dept. of Math. & Stat., Univ. of Calgary, July 1986. 129 + 19 pp. Second preliminary ed., slightly retitled: Sources in Recreational Mathematics and Queries on "Sources in Recreational Mathematics", Poly. of the South Bank, July 1987, 152 + 21 pp. Third preliminary ed., Dept. of Computing and Maths., Poly. of the South Bank, July 1988, 192 & 23 pp. Fourth preliminary ed. of the Sources only, slightly retitled: Sources in Recreational Mathematics. An Annotated Bibliography, Dept. of Computing and Maths., South Bank Poly, August 1989, 233 pp. Fifth preliminary ed., as above, November 1991, 313 pp. Sixth preliminary ed., School of Computing, Information Systems and Mathematics, South Bank University, November, 1993, 456 pp. Letter: Dissection of squares to rectangles. J. Recreational Math. 18:3 (1985/86) 227. Letter: More on zeros in factorials. J. Recreational Math. 18:1 (1985/86) 52. A new approach to n-person games. In: Abstracts - International Congress of Mathematicians, Berkeley, 1986, p. 316. How to Solve Rubik's Magic. Bunch Publishers, London, 1986. 32pp. Jointly with David Pritchard. Foreword, p. vii, and Appendix A: A mathematical note, pp. 231-232. In: Edward Hordern; Sliding Piece Puzzles; Oxford Univ. Press, 1986. xiv + 249 pp. 1987. [Keplerian pattern.] Pattern used in: Ralph P. Boas; Invitation to Complex Analysis; Random House/Birkh„user, NY, 1987, pp. 233 & 237. (Originally in: London Math. Soc. Newsletter 122 (Oct 1985) 12.) Letter: Sources in recreational mathematics. Math. Spectrum 19:1 (1986/87) 28. Letter: Cruellest month? M500 103 (1987) 8. [On start of the year.] Sources in recreational mathematics. Newsletter of the European Centre of the History of Medicine 17 (Jun 1987) 13. Non-symmetric equivalences of pentominoes. Idea used in: S. Fahri; Pentominoes; 6th ed., Pentacube Puzzles, New Zealand, 1981; problem 324, pp. 19 & 42. Also used in: Michael Keller; Contest Seven - Two piece non- symmetric equivalences; World Game Review 7 (Oct 1987) 13 & 30. Explorer's problem. Used in Keith Devlin's Micromaths column; The Guardian (18 Jun 1987) 16 & (2 Jul 1987) 16; collected in his book: All the Math That's Fit to Print, MAA, 1994, pp. 209-210 & 212. Used by Will Shortz in his National Public Radio program, Jan 1992. Used as: A walk on the wild side, Games 15:2 (No. 104) (Aug 1991) 57 & 40. 1988. Some early sources in recreational mathematics. In: Mathematics from Manuscript to Print. Ed. by C. Hay, et al. Oxford Univ. Press, 1988, pp. 195-208. Little Julie's confusing calculations. Math. Spectrum 20:3 (1987/88) 91. The number of square tilings. Micromath 4:2 (Summer 1988) 46-47. How not to cancel? Math. Spectrum 20:1 (1987/88) 13. Four-coloured chessboard - generalised solution of Problem 101.4. M500 104 (Nov 1988) 1. The trains and the fly. Math. Spectrum 20:2 (1987/88) 54. Duodecimals in antiquity. The Duodecimal Bulletin 31; : 1; (No. 59;) (1988) 14;, 16;, 18; (i.e. 16, 18, 20). Translation and series editor of: E. Rubik, et al.; Rubik's Cubic Compendium; Oxford Univ. Press, 1987, xi + 225pp. I wrote the original Introduction: The fascination of Rubik's Cube, pp. vii-xi, and added Chapter 7: Afterword, pp. 191-218. Antiquity revisited - A Reply. The Duodecimal Bulletin 31; : 2; (No. 5*;) (1988) #;-13;, 1*; (i.e. 11-15, 22). Old and new recreations in mathematics. In: Proceedings of the conference: Mathematics Teaching 1988, Univ. of Edinburgh, 1988, pp. 4-5. Report of Topic Area 11: Mathematical Games and Recreations. In: Proceedings of the Sixth International Congress on Mathematical Education; ICMI Secretariat & J nos Bolyai Mathematical Society, Budapest, 1988, pp. 361-364. 1988 - continued. Sources in recreational mathematics. British Society for the History of Mathematics Newsletter 9 (Oct 1988) 6. The frog and the snake. Math. Spectrum, 21:3 (1988/89) 84. 1989. The jealous husbands and the missionaries and the cannibals. Math. Gaz. 73 (No. 464) (Jun 1989) 73-81. [Longer version available from David Singmaster.] Jointly with Ian Pressman. From our own correspondent. Southbank News 39 (May 1989) 2. Letter from China. South Bank Poly, 1989, 62pp. 1990. The wobbler. Eureka 50 (1990) 74-78. Jointly with Rick Flowerday. Triangles with integer sides and sharing barrels. College Math. J. 21 (1990) 278-285. Growing plants. Math. Spectrum 23:1 (1990/91) 6. Latest research. Polymath [Newsletter of my Department] NS 4 (1990) 1. Painting cubes again. M500 114 (1989) 15. 1991. Triangles with equivalent relations between the angles and between the sides. With Mogens Esrom Larsen. Preprint Series 1991, No. 6, Apr 1991, 15pp, K›benhavns Univ., Mat. Inst. Missouri J. Math. Sci. 3 (1991) 111-123. Letter: Quotations on round pegs in square holes, etc. Theta 5:1 (1991) 36. Sources in Recreational Mathematics. An Annotated Bibliography. Fifth preliminary ed., Dept. of Computing and Maths., South Bank Poly., Nov 1991, 311 pp. The probability of finding an adjacent pair in a deck. Math. Gaz. 75 (No. 473) (Oct 1991) 293-299. Integer roots of integer polynomials. Crux Math. 17:7 (Sep 1991) 204- 205. Corner polyominoes. Math. Spectrum 24:4 (1991/92) 118. Comment on Problem 124.1: Card shuffle. M500 125 (Dec 1991) 11. [Probability of finding any adjacent pair.] Proposed by Anne Bates. 1992. Problems to sharpen the young. An annotated translation of Propositiones ad acuendos juvenes, attributed to Alcuin of York. Translated by John Hadley. With comments by David Singmaster and John Hadley. Math. Gaz. 76 (No. 475) (Mar 1992) 102-126. Books on Recreational Mathematics. A Supplement to the Lists in William L. Schaaf's A Bibliography of Recreational Mathematics. Collected by William L. Schaaf. Typed and annotated by David Singmaster. School of Computing, Information Systems and Mathematics, South Bank University, 19pp, 1992. Most wanted reprints. British Society for the History of Mathematics Newsletter 20 (Summer 1992) 10-11. Letter: Growing plants and Chinese mathematics. Math. Spectrum 24:3 (1991/92) 86-87. Letter on drilling square holes. The Guardian (27 Apr 1992) 19. Collected in: Notes & Queries, vol. 3; ed. by Brian Whitaker; Fourth Estate Ltd, London, 1992, p. 193. Report on Babbage and Lovelace plaques. British Society for the History of Mathematics Newsletter 20 (1992) 7. Letter: History of the decimal system. Theta 6 (1992) 33-34. Cylindrical and toroidal noughts and crosses. Math. Spectrum 25 (1992/93) 15. Letter: The Ramanujan problem. Math. Spectrum 25 (1992/93) 26. Walter William Rouse Ball (1850-1925). 6pp handout for my lecture at the First UK Meeting on the History of Recreational Mathematics, South Bank Univ., London, 24 Oct 1992. Plus 11pp of additional details. School of Computing, Information Systems and Mathematics, South Bank University, 1992. [I have proposed a DNB entry for Rouse Ball.] Square colouring. Mathematics Review 3:2 (Nov 1992) 23 & 29. Mathematical Monuments. School of Computing, Information Systems and Mathematics, South Bank University, Nov 1992, 112pp. (Revised in 1993 and 1995.) 1992 - continued. Piece of pi. M500 130 (Nov 1992) 11. Comment on Ralph Beauclerk; Calculation of pi by the Gregory series, M500 129 (Oct 1992) 6. FFF #54: A degree of differentiation. College Math. J. 23:3 (May 1992) 203; 23:4 (Sep 1992) 306. 1993. Books on Recreational Mathematics, etc. [Catalogue of my collection.] School of Computing, Information Systems and Mathematics, South Bank University, Jan 1993, 95pp. Some diophantine recreations. In: Articles in Tribute to Martin Gardner; ed. by Scott Kim for the opening of the exhibition: Puzzles: Beyond the Borders of the Mind at the Atlanta International Museum of Art and Design, 16 Jan 1993, pp. 343-356. Popmaths counts. Mathematics Review 3:3 (Feb 1993) 19 & 29. Puzzles: Beyond the Borders of the Mind and A Gathering for Gardner. Report of the exhibition opening and gathering in Atlanta, Jan 1993. Cubism for Fun 31 (Jun 1993) 25-30 & 32 (Aug 1993) 20. Foreword to Mathematics Resource Guide No. 5: Recreational Mathematics. QED Publications, York, 1993, pp. 3-4. Sliding Block Puzzle Circular No. 1. School of Computing, Information Systems and Mathematics, South Bank University, 9pp., May 1993. Revised to 10pp., Aug 1993. Sliding Block Puzzle Circular No. 2. School of Computing, Information Systems and Mathematics, South Bank University, 4pp., Sep 1993. Letter [on falling through the earth]. The Guardian (4 Jun 1993) 15. The history of recreational mathematics South Bank University 24 October 1992 (Report of meeting). British Society for the History of Mathematics Newsletter 23 (Spring 1993) 6-8. Unsigned, adapted from my report. Report of research in progress. British Society for the History of Mathematics Newsletter 24 (Summer 1993) 23-24. Index to Martin Gardner's Columns and Cross Reference to His Books. School of Computing, Information Systems and Mathematics, South Bank University, 23pp, Oct 1993. Sources in Recreational Mathematics - An Annotated Bibliography. 6th preliminary edition. School of Computing, Information Systems and Mathematics, South Bank University, Nov 1993, 456pp. Mathematical Monuments. School of Computing, Information Systems and Mathematics, South Bank University, Oct 1993, 87pp. (Revision of 1992 version. Revised in 1995.) Triangulated rectangles. Cubism for Fun 32 (Aug 1993) 32. With Dario Uri. The Daily Telegraph Braintwisters No. 1. Pan Books, London, 1993. With Barry R. Clarke, Rex Gooch and Angela Newing. Article 12.3: Recreational mathematics. In: Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences, ed. by I. Grattan- Guinness, Routledge, 1993, pp. 1568-1575. Article 12.12: Monuments to mathematics and mathematicians. Ibid., pp. 1659-1664. Coconuts. The history and solutions of a classic Diophantine problem. Technical Report SBU-CISM-93-02, School of Computing, Information Systems and Mathematics, South Bank Univ., Dec 1993, 15pp. ’kvivalente relationer mellem vinkler og sider i en trekant [in Danish]. Normat 41:4 (1993) 144-155, with English summary on p. 188. This is a somewhat revised and slightly expanded version of our 1991 paper, put into Danish by my co-author: Mogens Esrom Larsen. 1994. The utility of recreational mathematics. Presented at the Strens Memorial Conference, Calgary, 1986. In: The Lighter Side of Mathematics, ed. by Richard K. Guy and Robert E. Woodrow; MAA, 1994, pp. 340-345. Sliding Block Puzzle Circular No. 3. School of Computing, Information Systems and Mathematics, South Bank University, 2pp., Jan 1994. Unsolved problems. M500 136 (Jan 1994) 4-5. Unsolved problems 2. M500 137 (Apr 1994) 9. Letter: The Smarandache function - a previous existence. Math. Spectrum 2:3 (1993/4) 90. Chronology of Computing. Version of 4 Mar 1994. Technical Report SBU- CISM-94-05 (erroneously printed 95-05), School of Computing, Information Systems and Mathematics, South Bank Univ., Mar 1994, 70pp. Pegs and holes. Plus 26 (Spring 1994) 14-15 & 27 (Summer 1994) 23. Adapted by the editors from material sent by me and published with no byline. 1994 - continued. Don't believe your eyes. Focus (Dec 1994) 18-21. Arms and the University, part 2 [on the University arms and the Penrose pieces]. South Bank News (Autumn 1994) 30. Letter [on history of morris games]. Games & Puzzles No. 8 (Nov 1994) 31. The Bibliography of Some Recreational Mathematics Books. Technical Report SBU-CISM-94-09, School of Computing, Information Systems and Mathematics, South Bank University, Nov 1994, 39pp. Books on Recreational Mathematics. [Catalogue of my collection.] Technical Report SBU-CISM-94-11. School of Computing, Information Systems and Mathematics, South Bank University, Dec 1994, 110pp. Some 19th-century recreational mathematics books and their connections. British Society for the History of Mathematics Newsletter 27 (Aut 1994) 10. Report of erection of Lovelace Blue Plaque. British Society for the History of Mathematics Newsletter 25-26 (Spring-Summer 1994) 19. 1995. Determination of all pan-digital sums with two summands. J. Recreational Math. 27:3 (1995) 183-190. Spots puzzle re-revisited. Cubism for Fun 36 (Feb 1995) 16-17. Letter [on five touching balls]. Games & Puzzles No. 10 (Jan 1995) 27. Letter: Crossing deserts. Math. Spectrum 27:3 (1994/5) 63. Letter: Kepler's polygonal well. Math. Spectrum 27:3 (1994/5) 63-64. Notes on the History of Science and Technology in London. Technical Report SBU-CISM-95-27 (originally printed as -07). School of Computing, Information Systems and Mathematics, South Bank University, Jul 1995, 148pp. Quelques divertissements num‚riques. La Recherche 26 (No. 278) (Jul- Aug 1995) 818-823. = Algunos pasatiempos num‚ricos. Mundo Cientifico 15 (No. 161) (Oct 1995) 884-889. The Bibliography of Some Recreational Mathematics Books. 2nd ed. Technical Report SBU-CISM-95-08, School of Computing, Information Systems and Mathematics, South Bank University, Aug 1995, 41pp. Index to Martin Gardner's Columns and Cross Reference to His Books. Revised. Technical Report SBU-CISM-95-09, School of Computing, Information Systems and Mathematics, South Bank University, 22pp, Aug 1995. Sliding Block Puzzle Circular No. 4. 8pp. School of Computing, Information Systems and Mathematics, South Bank University. Typed and circulated in Aug 1995. Arithmetic progressions adding to a given sum. THETA 9:2 (Autumn 1995) 23-28. A Mathematical Gazetteer. Technical Report SBU-CISM-95-10. School of Computing, Information Systems and Mathematics, South Bank University, Oct 1995, 136pp. (Revision of Mathematical Monuments, 1993.) Letter [on Joseph Lancaster]. Update (South Bank University) 36 (Oct 1995) 2. Letter [on snakes and ladders]. Math. Gaz. 79 (No. 485) (Jul 1995) 396-397. Letter [on the International Date Line]. Notes and Queries column, The Guardian, section 2 (20 Dec 1995) 7. Reprinted in Guardian Weekly (7 Jan 1996) 24. 1996. Symmetry saves the solution. IN: Alfred S. Posamentier & Wolfgang Schulz, eds.; The Art of Problem Solving: A Resource for the Mathematics Teacher; Corwin Press, NY, 1996, pp. 273-286. (I also provided much of the material in: Sources for Problems, pp. 445-452, and Readings on Problem Solving, pp. 453-456.) Coconuts. The history and solutions of a classic Diophantine problem. Revised and reformatted to 15pp + 4pp illustrations, 17 Jan 1996. Presented at 2nd Gathering for Gardner, Atlanta, 19 Jan 1996. Slightly amended 29 Apr 1996 and printed as Technical Report SBU-CISM-96-08, 15pp + 4pp illustrations + 1 separate p. of additions. The Bibliography of Some Recreational Mathematics Books. 3rd ed. Technical Report SBU-CISM-96-12, School of Computing, Information Systems, and Mathematics, South Bank University, Jun 1995, 42pp. Proceedings of the First UK Meeting on the History of Recreational Mathematics. At South Bank University, 24 October 1992. Papers by John D. Beasley, R. C. Bell, C. G. Lewin, David Singmaster. Edited by David Singmaster. Technical Report SBU-CISM-96-09. School of Computing, Information Systems and Mathematics, South Bank University, May 1996, 45pp. Letter [on Piet Hein's death]. The Guardian (11/12 May 1996) 28. Chronology of Computing Version of 19 Jun 1996. Technical Report SBU- CISM-96-11, School of Computing, Information Systems and Mathematics, South Bank Univ., Jun 1996, 71pp. SERIES BBC Radio 5 - Mathematics Miscellany. Program on p and five short problems, used in 1990. Contributor to a program on African mathematics, 1992. Presenter of The Puzzle Room, 4 Apr 1993. More material recorded in Mar 1995. Contributor (uncredited!) to The Square on the Pythagoras, BBC Radio 4, 11 & 15 Nov 1995. Mathematical Gazetteer of Britain. British Society for the History of Mathematics Newsletter. Beginning in No. 28 (Spring 1995). See Editorial, ibid., p. 3. #1 Aberdeen to Ashford. No. 28 (Spring 1995) 28-29. #2 Barnard Castle to Byers Green. No. 29 (Summer 1995) 10-16. #3 Cambridge part 1 (Institutions). No. 30 (Autumn 1995) 31-37. Canadian Broadcasting Corp. - Quirks & Quarks. 5 short puzzles, broadcast Spring 1987. 10 short puzzles, recorded Sep 1990. 11 short puzzles, recorded Aug 1994. Cubic Circular. No. 1, Dec 1981, 16pp. No. 2, Apr 1982, 16pp. No. 3/4, Jul 1982, 36pp. No. 5/6, Dec 1982, 28pp. No. 7/8, Aug 1985, 48pp. Recreations in Mathematics Series, Oxford Univ. Press. Series editor. 1. Hugh ApSimon. Mathematical Byways in Ayling, Beeling and Ceiling. 1984. xiv + 97 pp. 2. J. D. Beasley. The Ins and Outs of Peg Solitaire. 1985. 275pp. 3. E. Rubik, et al. Rubik's Cubic Compendium. 1987. xi + 225pp. I wrote the original Introduction: The fascination of Rubik's Cube, pp. vii-xi [See 1981], edited the translation and provided Chapter 7: Afterword, pp. 191-218. 4. Edward Hordern. Sliding Piece Puzzles. 1986. xiv + 249 pp. I wrote the Foreword, p. vii, and Appendix A: A mathematical note, pp. 231- 232. 5. J. D. Beasley. The Mathematics of Games. 1989. 192 pp. 6. Stewart T. Coffin. The Puzzling World of Polyhedral Dissections. 1990. 204pp. 7. Hugh ApSimon. More Mathematical Byways in Ayling, Beeling and Ceiling. 1990, 128pp. Sliding Block Puzzle Circular. School of Computing, Information Systems and Mathematics, South Bank University. No. 1, 9pp., May 1993. Revised to 10pp., Aug 1993. No. 2, 4pp., Sep 1993. No. 3, 2pp., Jan 1994. No. 4, 8pp., Aug 1995. PUZZLE COLUMNS Focus. Brain Teasers page - Puzzles. From Issue 1, Dec 1992 until Issue 21, Aug 1994. Some reuse of Weekend Telegraph material, others previously unused, averaging two puzzles per issue. 26 puzzles used. Games & Puzzles The Puzzle Box. Started with No. 11, Feb 1995. Answers in the following month. 46 puzzles used through Jul 1995 when the magazine closed. Los Angeles Times. Enigma column, alternating with S. W. Golomb. In Section CC/Part II on Mondays, p. 3, with solution on p. 8, beginning on 28 Sep 1987. About 30 puzzles used before this ceased. MSC News/Polymaths - Newsletter of my Department. Name changed to Polymaths with issue 4. Puzzle column starting with issue 1 (Apr 1986), 16 puzzles used before the Newsletter ceased. Weekend Telegraph. Brain Twister column, shared with three others. This is the second section of The Daily Telegraph on Saturdays. From 27 Feb 1988 through 2 Apr 1994. 94 problems appeared. A book appeared in Dec 1993. I have contributed numerous proposals, solutions and comments on problems and on other mathematical matters to the following: American Mathematical Monthly, Bulletin of the Institute of Mathematics and Its Applications, Crux Mathematicorum, Fibonacci Quarterly, Games, Games & Puzzles, The Guardian, Historia Mathematica, Journal of Recreational Mathematics, Lincolnshire Echo, Mathematical Gazette, Mathematical Spectrum, Mathematics Magazine, Mathematics Review, M500, Nature, QARCH, SIAM Review, South Bank News and THETA. REVIEWS Bernard Kolman; Introductory Linear Algebra with Applications and William S. Dorn & Daniel D. McCracken; Introductory Finite Mathematics with Computing. Times Higher Educ. Supp. (12 Nov 1976) 23. Norman L. Biggs, E. Keith Lloyd & Robin J. Wilson; Graph Theory 1736- 1936. Times Higher Educ. Supp. (24 Dec 1976) 16. Derek I. Bloomfield; From Arithmetic to Algebra. Science Books & Films 12:4 (Mar 1977) 194. Michael O'Nan; Linear Algebra, 2nd ed.; Harcourt, Brace, Jovanovich, 1976. Times Higher Educ. Supp. (12 Aug 1977) 21. G. Birkhoff & S. Mac Lane; A Survey of Modern Algebra, 4th ed.; Macmillan, 1977. Times Higher Educ. Supp. (14 Oct 1977) 20. Seven Bridges of Konigsberg and Turning a Sphere Inside Out. British Universities Film Council Newsletter 32 (Nov 1977) 19. Math, bees and infinity. Times Higher Educ. Supp. (16 Dec 1977) 18. [Reviews of mathematical films.] George E. Andrews; The Theory of Partitions; Addison-Wesley, 1976 and William C. Swift & David E. Wilson; Principles of Finite Mathematics; Prentice Hall, 1977. Science Books & Films 14:1 (May 1978) 14 & 16-17. Gilbert Strang; Linear Algebra and Its Applications; Academic Press. Times Higher Educ. Supp. (3 Feb 1978) 23. Robert R. Arnold, Harold C. Hill & Aylmer V. Nichols; Modern Data Processing, 3rd ed., Wiley, NY, 1978 and J. M. Dubbey; The Mathematical Work of Charles Babbage; Cambridge Univ. Press, NY, 1978. Science Books & Films 14:4 (Mar 1979) 203 & 212 resp. J. D. Tarwater, ed.; The Bicentennial Tribute to American Mathematics; Math. Assoc. of America, Washington, 1977. Math. Gaz. 63 (No. 425) (Oct 1979) 203-205. B‚la Andr sfai; Introductory Graph Theory; Adam Hilger, Bristol, 1977. Internat. J. Math. Ed. Sci. Tech. 10:3 (1979) 471-472. Daniel I. A. Cohen; Basic Techniques of Combinatorial Theory; Wiley, 1979. Math. Gaz. 64 (No. 428) (Jun 1980) 139-140. Marvin Jay Greenberg; Euclidean and Non-Euclidean Geometries: Development and History; 2nd ed., Freeman, 1980. Math. Gaz. 66 (No. 436) (1982) 172-173. The classics of 1982. New Scientist 97 (No. 1339) (6 Jan 1983) 40. [Appreciation of Winning Ways, by E. R. Berlekamp, J. H. Conway & R. K. Guy.] H. Rademacher; Higher Mathematics from an Elementary Point of View; Birkh„user, 1983. Math. Gaz. 68 (No. 445) (Oct 1984) 234-235. All in the mind - review of: Steven B. Smith; The Great Mental Calculators; Columbia Univ. Press, NY, 1983. Nature 310 (No. 5972) (5 Jul 1984) 79-80. Further problems of entertainment - review of: Martin Gardner; Wheels, Life and Other Mathematical Amusements; Freeman, San Francisco, 1983. Nature 310 (No. 5977) (9 Aug 1984) 521. Alan Baker; A Concise Introduction to the Theory of Numbers; Cambridge Univ. Press, Cambridge, 1984. Math. Gaz. 69 (No. 450) (Dec 1985) 318-319. Caption review of: Gerd Fischer, et al.; Mathematical Models; Vieweg, Wiesbaden, 1986. Nature 322 (3 Jul 1986) 25. E. F. Clark; George Parker Bidder - The Calculating Boy; With an Appreciation of His Calculating Ability by Joyce Linfoot; KSL Publications, Bedford, 1983. Math. Gaz. 71 (No. 457) (1987) 252-254. Donald J. Albers, G. L. Alexanderson & Constance Reid; International Mathematical Congresses - An Illustrated History 1893-1986; revised ed., Springer-Verlag, NY, 1987. Math. Gaz. 72 (No. 460) (Jun 1988) 166-167. S. Mac Lane & G. Birkhoff; Algebra, 3rd ed.; Chelsea, NY, 1988. Math. Gaz. 75 (No. 471) (Mar 1991) 121. Charles Tanford; Ben Franklin Stilled the Waves: An Informal History of Pouring Oil on Water with Reflections on the Ups and Downs of Scientific Life in General; Duke Univ. Press, Durham, NC, 1989. The Clapham Antiquarian No. 504 (Apr 1992) 2-4. Arthur C. Clarke's Colours of Infinity: Exploring the Fractal Universe, a 53 min. video. Viewfinder (The British Universities Film & Video Council Magazine) No. 24 (May 1995) 11. TO APPEAR An elementary volume problem. Amer. Math. Monthly - after some revision. Which base is best? Colson News. The n-dimensional law of cosines. Mathematics in College - after some revision. The History of some of Alcuin's Propositiones. Presented at: Colloquium Carolus Magnus - 1200 Jahre Wissenschaft in Zentral-Europa, Aachen, Mar 1995. Article to appear in the Proceedings, 1996? The hundred fowls, or how to count your chickens. Math. Spectrum - after some abridgement. SUBMITTED A cubical path puzzle. J. Recreational Math. Hamiltonian circuits on regular polyhedra - comments on Arisawa's "Around the world in four dimensions". J. Recreational Math. Design for a ceremonial staircase. Perception. New cube dissection puzzles. J. Recreational Math. On cuboidal dice. J. Recreational Math. Proposals for DNB entries for W. W. R. Ball and H. Phillips. BEING REVISED The hundred fowls, or how to count your chickens. Sum = product sequences. Jointly with Mike Bennett and Andrew Dunn. Bear hunting problems. Generalized diagonal sums in Pascal's triangle. Presented at 5th Internat. Conf. on Fibonacci Numbers, St. Andrews, 1992. IN PREPARATION Notes on binomial coefficients - V. The proportion of three consecutive binomial coefficients. Notes on binomial coefficients - VI. On a problem of Babbage. (See: D. Wells; Penguin Dictionary of Curious and Interesting Numbers; p. 175.) The last non-zero digit of n! - a new random number generator. The nets of the regular polyhedra. Jointly with P. Light. The distribution of products (mod m). On n player combinatorial games. Pick's theorem - by Pick. Direct derivations for the number of unordered selections with repetitions and the m‚nage lemmas. The number of inversions in a permutation and a coin-tossing problem. Is left really right? - Reasons for driving on the left. Book on binomial coefficients. Documentation for a polyhedral display package. Cigarette butts. Integer sided lattice triangles are the same as Heronian triangles. With Dick Hess and John Silvester.

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