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---------- Forwarded message --------- From: R-bloggers <[email protected]> Date: Mon, Jun 17, 2019 at 6:13 PM Subject: [R-bloggers] Le Monde puzzle [#1104] To: <[email protected]> [R-bloggers] Le Monde puzzle [#1104] <https://www.r-bloggers.com> [image: Link to R-bloggers] <https://www.r-bloggers.com> ------------------------------ Le Monde puzzle [#1104] <http://feedproxy.google.com/~r/RBloggers/~3/Dhdp0uFh-WA/?utm_source=feedburner&utm_medium=email> Posted: 17 Jun 2019 03:19 PM PDT <https://twitter.com/share> (This article was first published on * R – Xi'an's Og <https://xianblog.wordpress.com/2019/06/18/le-monde-puzzle-1104/>*, and kindly contributed to R-bloggers) <https://www.r-bloggers.com/> *A* palindromic Le Monde mathematical puzzle <https://xianblog.wordpress.com/2011/09/03/le-monde-puzzle-website/>: *In a monetary system where all palindromic amounts between 1 and 10⁸ have a coin, find the numbers less than 10³ that cannot be paid with less than three coins. Find if 20,191,104 can be paid with two coins. Similarly, find if 11,042,019 can be paid with two or three coins. * Which can be solved in a few lines of R code: coin=sort(c(1:9,(1:9)*11,outer(1:9*101,(0:9)*10,"+"))) amounz=sort(unique(c(coin,as.vector(outer(coin,coin,"+"))))) amounz=amounz[amounz<1e3] and produces 10 amounts that cannot be paid with one or two coins. It is also easy to check that three coins are enough to cover all amounts below 10³. For the second question, starting with n¹=20,188,102, a simple downward search of palindromic pairs (n¹,n²) such that n¹+n²=20,188,102 led to n¹=16,755,761 and n²=3,435,343. And starting with 11,033,011, the same search does not produce any solution, while there are three coins such that n¹+n²+n³=11,042,019, for instance n¹=11,022,011, n²=20,002, and n³=6. To *leave a comment* for the author, please follow the link and comment on their blog: * R – Xi'an's Og <https://xianblog.wordpress.com/2019/06/18/le-monde-puzzle-1104/>*. ------------------------------ R-bloggers.com <https://www.r-bloggers.com/> offers *daily e-mail updates <https://feedburner.google.com/fb/a/mailverify?uri=RBloggers>* about R <https://www.r-project.org/> news and tutorials <https://www.r-bloggers.com/search/tutorial> on topics such as: Data science <https://www.r-bloggers.com/search/data%20science>, Big Data, <https://www.r-bloggers.com/search/Big%20Data>R jobs <https://www.r-users.com/>, visualization (ggplot2 <https://www.r-bloggers.com/search/ggplot2>, Boxplots <https://www.r-bloggers.com/search/boxplot>, maps <https://www.r-bloggers.com/search/map>, animation <https://www.r-bloggers.com/search/animation>), programming (RStudio <https://www.r-bloggers.com/search/RStudio>, Sweave <https://www.r-bloggers.com/search/sweave>, LaTeX <https://www.r-bloggers.com/search/LaTeX>, SQL <https://www.r-bloggers.com/search/SQL>, Eclipse <https://www.r-bloggers.com/search/eclipse>, git <https://www.r-bloggers.com/search/git>, hadoop <https://www.r-bloggers.com/search/hadoop>, Web Scraping <https://www.r-bloggers.com/search/Web+Scraping>) statistics (regression <https://www.r-bloggers.com/search/regression>, PCA <https://www.r-bloggers.com/search/PCA>, time series <https://www.r-bloggers.com/search/time+series>, trading <https://www.r-bloggers.com/search/trading>) and more... You are subscribed to email updates from R-bloggers <https://www.r-bloggers.com>. To stop receiving these emails, you may unsubscribe now <https://feedburner.google.com/fb/a/mailunsubscribe?k=42gkTfZCc6B-nnx1AjmwNPM5E-w> . Email delivery powered by Google Google, 1600 Amphitheatre Parkway, Mountain View, CA 94043, United States ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
