# Solving the rectangle puzzle

**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.

**G**iven the wrong solution provided in Le Monde and comments from readers, I went to look a bit further on the Web for generic solutions to the rectangle problem. The most satisfactory version I have found so far is Mendelsohn’s in * Mathematics Magazine*, which gives as the maximal number

for a grid. His theorem is based on the theory of projective planes and must be such that a projective plane of order exists, which seems equivalent to impose that is a prime number. The following graph plots the pairs when along with the known solutions, the fit being perfect for the values of of Mendelsohn’s form (i.e., 3, 7, 13).

**U**nfortunately, the formula does not extend to other values of , despite Menselsohn’s comment that *using for the positive root of the equation and then replacing by nearby integers* (in the maximal number) should work. (The first occurrence I found of a solution for a square-free set did not provide a generic solution, but only algorithmic directions. While it is restricted to squares. the link with fractal theory is nonetheless interesting.)

Filed under: Kids, R Tagged: fractal, Le Monde, mathematical puzzle, Mendelsohn, primes, projective planes

**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.