Le Monde puzzle [#939]

December 10, 2015

(This article was first published on Xi'an's Og » R, and kindly contributed to R-bloggers)

A Le Monde mathematical puzzle about special integers:

Find all integers with less than 11 digits that are perfect squares and can be written as a(a+6), a being an integer.

Eleven digits being too much for a brute force exploration of the form `for (t in 1:1e11)`…, some preliminary  analysis is needed, but I could not figure out a reason why there is no solution apart from 2… (I checked up to 1e8!)

Since I had “guessed” the above puzzle from the solution published one week later (!), I checked the quality of my guesswork with my friend Jean-Louis Fouley, who gave me the genuine question, based on a different interpretation of a(a+6):

Find all integers with less than 11 digits that are perfect squares and can be written as x concatenated with (x+6), x being an integer.

This is more open to brute-force R exploration (with some help from stack overflow) since x only has five digits at most!

  for (i in a:(a+1))
    if (i^2==b) x=TRUE

for (x in 1:(1e6-1))
  if (perfect(
    as.numeric(paste(c(as.numeric(strsplit(as.character(x), "")[[1]]),
    as.numeric(strsplit(as.character(x+6), "")[[1]])),collapse="")))) 

Which returns

[1] 15
[1] 38

and then crashes for x=99994, because

strsplit(as.character(1e+05), "") 

does not return the six digits of 1e+05 but

[1] "1" "e" "+" "0" "5"

instead. Except for this value of x, no other solution is found using this R code. And for x=99994, y=99994100000 is not a perfect square.

Filed under: Books, Kids, R Tagged: arithmetics, as.character(), as.numeric(), Le Monde, mathematical puzzle, R, strsplit()

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

R-bloggers.com offers daily e-mail updates about R news and tutorials on topics such as: Data science, Big Data, R jobs, visualization (ggplot2, Boxplots, maps, animation), programming (RStudio, Sweave, LaTeX, SQL, Eclipse, git, hadoop, Web Scraping) statistics (regression, PCA, time series, trading) and more...

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


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)