Le Monde puzzle [#1075]

November 21, 2018
By

[This article was first published on R – Xi'an's Og, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)
Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

A Le Monde mathematical puzzle from after the competition:

A sequence of five integers can only be modified by subtracting an integer N from two neighbours of an entry and adding 2N to the entry.  Given the configuration below, what is the minimal number of steps to reach non-negative entries everywhere? Is this feasible for any configuration?

As I quickly found a solution by hand in four steps, but missed the mathematical principle behind!, I was not very enthusiastic in trying a simulated annealing version by selecting the place to change inversely proportional to its value, but I eventually tried and also obtained the same solution:

      [,1] [,2] [,3] [,4] [,5]
   -3    1    1    1    1
    1   -1    1    1   -1
    0    1    0    1   -1
   -1    1    0    0    1
    1    0    0    0    0

The second part of the question is more interesting, but again without a clear mathematical lead, I could only attempt a large number of configurations and check whether all admitted “solutions”. So far none failed.

To leave a comment for the author, please follow the link and comment on their blog: R – Xi'an's Og.

R-bloggers.com offers daily e-mail updates about R news and tutorials about learning R and many other topics. Click here if you're looking to post or find an R/data-science job.
Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.



If you got this far, why not subscribe for updates from the site? Choose your flavor: e-mail, twitter, RSS, or facebook...

Comments are closed.

Search R-bloggers

Sponsors

Never miss an update!
Subscribe to R-bloggers to receive
e-mails with the latest R posts.
(You will not see this message again.)

Click here to close (This popup will not appear again)