This is a gem of a puzzle from *A Moscow Math Circle, Week by Week Problem Sets* by Sergey Dorichenko.

Can a 10×10 square be paved with 1×4 rectangular stone plates?

As always, please send your answers as comments within the blog (preferred), or send an e-mail to alokgoyal_2001@yahoo.com. Please do share the puzzle with others if you like, and please also send puzzles that you have come across that you think I can share in this blog.

Happy paving!

The problem can be changed to:

Is it possible to have 50 numbers from [-40, 49] such that sum of no two numbers is 0.

[41,49] would not matter here

So, Is it possible to have 41 numbers from [-40, 40] such that sum of no two numbers is 0.

Not possible!

Hope you all enjoyed the puzzle!