

Jan 23, 2015

Box in Box problem

Source: Sent to me by Sudeep Kamath


Airline check-in baggage has size restriction by ​so-called ​linear dimension: length + breadth + height should not exceed 62 inches. Prove that you can't "cheat" by packing a box with higher linear dimension into a box with ​lower​ linear dimension.

Jan 21, 2015

Fibonacci Multiple Puzzle

Source: Mailed to me by Kushagra Singhal, Ex-IIT Kanpur, PhD Student at University of Illinois at Urbana-Champaign


Prove that for any positive K and a natural number n, every (n*K)th number in the Fibonacci sequence is a multiple of the Kth number in the Fibonacci sequence.

More formally, for any natural number n, let F(n) denote Fibonacci number n. That is, F(0) = 0, F(1) = 1, and F(n+2) = F(n+1) + F(n). Prove that for any positive K and natural n, F(n*K) is a multiple of F(K).

Jan 19, 2015

Gold Silver Numbers Puzzle

Source: Mailed to me by JDGM ("regular commenter JDGM")


The integers greater than zero are painted such that:

• every number is either gold or silver.
• both paints are used.
• silver number + gold number = silver number
• silver number * gold number = gold number

Given only this information, for each of the following decide whether it is a gold number, a silver number, or could be either:

1.) gold number * gold number
2.) gold number + gold number
3.) silver number * silver number
4.) silver number + silver number