Hostname: page-component-7b7567c8c-lpg2g Total loading time: 0 Render date: 2026-11-15T19:51:54.871Z Has data issue: false hasContentIssue false
  • English
  • Français

A probabilistic way to discover the rainbow

Published online by Cambridge University Press:  24 February 2022

Joscha Prochno and
Michael Schmitz
Joscha Prochno
Affiliation:
Faculty of Computer, Science and Mathematics, University of Passau, Innstrasse 33, 94032 Passau, Germany e-mail: joscha.prochno@uni-passau.de
Michael Schmitz
Affiliation:
University of Flensburg, Auf dem Campus 1, 24943 Flensburg, Germany, e-mail: michael.schmitz@uni-flensburg.de

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

A slogan that you find on the back of a pack of Skittles candy says ‘No two rainbows are the same. Neither are two packs of Skittles. Enjoy an odd mix.’ An online blog [1] describes how the blogger found two identical packs of Skittles, among 468 packs with a total of 27,740 Skittles. Meticulously collecting the data for this experiment was apparently triggered by some earlier calculations. More precisely, the blogger writes:

Information

Type
Articles
Information
The Mathematical Gazette , Volume 106 , Issue 565 , March 2022, pp. 103 - 115
Check for updates
Copyright
© The Authors, 2022. Published by Cambridge University Press on behalf of The Mathematical Association

References

PossiblyWrong. Follow-up: I found two identical packs of Skittles, among 468 packs with a total of 27,740 Skittles, accessed 06/12/2021 at https://possiblywrong.wordpress.com/2019/04/06/follow-up-i-found-two-identical-packs-of-skittles-among-468-packs-with-a-total-of-27740-skittles/ Google Scholar
Feller, W., An Introduction to Probability Theory and Its Applications (Vol. 1, 3rd edn.), New York: John Wiley (1968).Google Scholar
Schwarz, W., Approximating the Birthday Problem, The American Statistician, 42 (3) (August 1988) pp. 195–196.Google Scholar
Perkins, W., Inequalities, Birthday, Repulsion, and hard Spheres, Proc. Amer. Math. Soc. 144 (2016) pp. 2635–2649.10.1090/proc/13028CrossRefGoogle Scholar
Mathoverflow, Birthday inequality for non-uniform distributions for fixed collision probability, accessed on 06/12/2021. https://mathoverflow.net/questions/257027/birthday-inequality-for-non-uniform-distributions-for-fixed-collision-probabilit Google Scholar
Bloom, D. M., A Birthday Problem, American Mathematical Monthly, 80 (1973) pp. 1141–1142.Google Scholar
Munford, A. G., A Note on the Uniformity Assumption in the Birthday Problem, The American Statistician, 31 (3) (August 1977) p. 119.Google Scholar
Nunnikhoven, T. S., A Birthday Problem Solution for Nonuniform Birth Frequencies, The American Statistician, 46 (4) (November 1992) pp. 270–274.Google Scholar
Wiener, M. J., Bounds on Birthday Attack Times, IACR Eprint archive, http://eprint.iacr.org/2005/318 (2005).Google Scholar