I recently watched this interesting video by Shai Avidan and Ariel Shamir from MERL. They developed an extremely cool image resizing technique called seam carving. They explain all about it in this article.
One of the coolest things about their idea is that is it easy to implement. I implemented a semi-optimized version of their algorithm in a couple of hours of coding. All the images in this post were generated by my code.
In this article you will find a collection of riddles. They are all either very well known or extremely easy. Enjoy!
Cutting the Cake
How can you cut a circular cake to eight even pieces with 3 cuts? What is the maximum number of pieces possible with 4 cuts?
When considering the extra-credit of the 23 and 2000 riddle, I thought of an additional interesting problem.
Let N be a positive integer. A partition of N into m parts (an m-partition of N) is a multiset of m positive integers, such that their sum equals N. A multiset is a set which may contain repeated elements.
You are given 23 whole numbers, not necessarily distinct, in a row.
You cannot change the order of the numbers.
Prove that there exists an arrangement of the symbols ’+’, ‘×’, ‘(’ and ‘)’ in-between the 23 numbers, such that the final result is a valid formula, whose evaluated value equals 0 mod 2000.
When I started yaniv.leviathanonline.com, I declared it to be a site about “Mathematics and Hacking”. As of now, most of its content is Mathematical. I thought it was time for a little change…