[This article was first published on 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.
Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.
Given a partition of the set {1,…,N} in k groups, one considers the collection of all subsets of the set {1,…,N} containing at least one element from each group. Show that the size of the collection cannot be 50.
Obviously, 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 n1,…,nk, 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.