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Recreational Mathematics Magazine

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Endless Love: On the Termination of a Playground Number Game

Iain G. Johnston
  • School of Biosciences, University of Birmingham, UK
  • :
Published Online: 2016-04-14 | DOI: https://doi.org/10.1515/rmm-2016-0005

Abstract

A simple and popular childhood game, loves or the love calculator, involves an iterated rule applied to a string of digits and gives rise to surprisingly rich behaviour. Traditionally, players’ names are used to set the initial conditions for an instance of the game: its behaviour for an exhaustive set of pairings of popular UK childrens’ names, and for more general initial conditions, is examined. Convergence to a fixed outcome (the desired result) is not guaranteed, even for some plausible first name pairings. No pairs of top-50 common first names exhibit non-convergence, suggesting that it is rare in the playground; however, including surnames makes non-convergence more likely due to higher letter counts (for example, “Reese Witherspoon loves Calvin Harris”). Difierent game keywords (including from difierent languages) are also considered. An estimate for non-convergence propensity is derived: if the sum m of digits in a string of length w obeys m > 18=(3=2/)w-4, convergence is less likely. Pairs of top UK names with pairs of ‘O’s and several ‘L’s (for example, Chloe and Joseph, or Brooke and Scarlett) often attain high scores. When considering individual names playing with a range of partners, those with no loves letters score lowest, and names with intermediate (not simply the highest) letter counts often perform best, with Connor and Evie averaging the highest scores when played with other UK top names.

Keywords: Number games; name statistics; dynamic integer sequences; mathematics in schools

References

  • [1] Bever, K., Rowlett, J. “Love Games: A Game Theory Approach to Com- patibility”, preprint, arXiv:1312.5483, 2013.

  • [2] Klawe, M., Phillips, E. “A classroom study: Electronic games engage children as researchers”, The first international conference on Computer sup- port for collaborative learning, L. Erlbaum Associates Inc., 209{213, 1995.

  • [3] Papadimitriou, C., Steiglitz, K. Combinatorial optimization: algorithms and complexity, Dover, 1998.

  • [4] Roud, S. The lore of the playground: One hundred years of children's games, rhymes and traditions, Random House, 2010.

  • [5] Love calculations and paper fortune-tellers retrieved from http://www.imisstheoldschool.com/archives/love-calculations-and-chatterbox at February, 2016.

  • [6] UK Office for National Statistics retrieved from http://www.ons.gov.uk/ons/rel/vsob1/baby-names--england-and-wales/2010/index.html at February, 2016.


Published Online: 2016-04-14

Published in Print: 2016-03-01


Citation Information: Recreational Mathematics Magazine. Volume 3, Issue 5, Pages 61–78, ISSN (Online) 2182-1976, DOI: https://doi.org/10.1515/rmm-2016-0005, April 2016

© 2016. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. (CC BY-NC-ND 4.0)

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