# Le Monde puzzle [#822]

[This article was first published on

Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

**Xi'an's Og » R**, 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.

**F**or once Le Monde math puzzle is much more easily solved on a piece of paper than in R, even in a plane from Roma:

Given a partition of the set {1,…,N} in k groups, one considers the collection of all subsets ofthe set {1,…,N} containing at least one element from each group. Show that the size of the collection cannot be 50.

**O**bviously, one could consider a range of possible N’s and k’s and run a program evaluating the sizes of the corresponding collections. However, if the k groups are of size n_{1},…,n_{k}, the number of subsets satisfying the condition is

and it is easily shown by induction that this number is necessarily odd, hence the impossible 50.

Filed under: Books, Kids, R Tagged: combinatorics, induction, Le Monde, mathematical puzzle, odd numbers, partition, R

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 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.