A Diffy Box Bibliography

NOTE TO READERS: My co-authors and I were informed about the extensive body of research that has been done to date on the diffy box problem under the name "Ducci 4-number game" only after our article had gone to press; prior to that time, our attempts (and presumably our reviewers') to research any earlier work on the topic was stymied by differences in terminology. We now see that this is not the first time this has happened for this topic, as some of the other papers in this area likewise fail to mention some of their predecessors. I was able to convince the editor to change three pages of the article proofs to incorporate at least one new reference and an acknowledgement that previous work had been done. Below I list a larger bibliography of related works, to which you should feel free to add by sending me e-mail at kribs(at)uta dot edu. Some papers address an aspect of the problem as posed in our paper; others consider variations, generalizations or related problems. My co-authors and I continue to feel that our approach to the problem offers something new.

Thanks for your interest.

Bibliography

O. Andriychenko and M. Chamberland (2000), Iterated Strings and Cellular Automata, Mathematical Intelligencer 22(4): 33-36.
E.R. Berlekamp (1975), The design of slowly shrinking labelled squares, Math. Comp. 29: 25-27.
F. Breuer (1998), A note on a paper by Glaser and Scho:ff, Fibonacci Quarterly 36(5): 463-466.
M. Chamberland (2003), Unbounded Ducci Sequences, Journal of Difference Equations and Applications 9: 887-895.
M. Chamberland and D. Thomas (2004), The N-Number Ducci Game -- Open Problems, Journal of Difference Equations and Applications 10: 339-342.
C. Ciamberlini and A. Marengoni (1937), Sa una interessante curiosit\`{a} numerica, Period. Mat. Ser. 4: 25-30.
A. Clausing (2004), Tribonacci in the sky: a mathematical mountain walk, Pi in the Sky 8: 28-31.
A. Ehrlich (1990), Periods in Ducci's n-number game of differences, Fibonacci Quarterly 28: 302-305.
B. Freedman (1948), The four number game, Scripta Math. 14: 35-47.
M. Gardner (1987), Riddles of the sphinx, MAA, Washington. Problem 29.
H. Glaser and G. Scho:ff (1995), Ducci-sequences and Pascal's triangle, Fibonacci Quarterly 33: 313-324.
R. Greenwell (1989), The game of Diffy, Math. Gazette 73: 222-225.
R. Honsberger (1970), Ingenuity in Mathematics, Random House, New York.
J.H. Jordan (1964), Self-producing sequences of digits, American Mathematical Monthly 71: 61-64.
M. Lotan (1949), A problem in difference sets, American Mathematical Monthly 56: 535-541.
A. Ludington-Young (1990), Length of the n-number game, Fibonacci Quarterly 28: 259-265.
K.R. McLean (1999), Playing Diffy with real sequences, Math. Gazette 83: 58-68.
L. Meyers (1982), Ducci's four-number problem: a short bibliography, Crux Mathematicorum 8: 262-266.
R. Miller (1978), A game with n numbers, American Mathematical Monthly 85: 183-185.
M. Misiurewicz and A. Schinzel (1988), On n numbers on a circle, Hardy-Ramanujan Journal 11: 30-39.
M. Misiurewicz, J.G. Stevens, D. Thomas (2006), Iterations of linear maps over finite fields, Linear Algebra Appl. 413: 218--234.
R. Sprague (1963), Recreation in mathematics, Dover, New York.
D. Thomas, N. Calkin and J. Stevens (2005), A characterization for the length of cycles of the N-Number Ducci Game, Fibonacci Quarterly Feb. 2005.
D. Ullman (1992), More on the Four-Numbers Game, Mathematics Magazine 65(3): 170-174.
W. Webb (1982), The length of the four-number game, Fibonacci Quarterly 20: 33-35.
P. Winkler (2003), Mathematical Puzzles: A Connoisseur's Collection, AK Peters, Natick, MA.

This page last updated 23 May 2005.