## Posts

Showing posts from July, 2014

### 3D Tic Tac Toe Puzzle

Source: Shared by Alok Mittal (Cannan Partners)
Problem: A 3x3 tic tac toe has 8 "winning lines" (3 horizontal, 3 vertical and 2 diagonals). How many "winning lines" does the 3x3x3 3D tictactoe have? There is a brute force solution, and then there is the aha! solution.

Update (23 Oct 2014)
Solution: Posted in comments by Anti, Taz, Javier, Shubham Gupta, Leela. Detailed solution and much more advanced problems in the document http://library.msri.org/books/Book42/files/golomb.pdf

### Mad Robot Puzzle

Source:http://nrich.maths.org/

Problem:

A mad robot sets off towards the North East on a journey from the point (0,0) in a coordinate system. It travels in stages by moving forward and then rotating on the spot. It follows these pseudo-code instructions:

SUB JOURNEY
DISTANCE = 1000
WHILE (DISTANCE > 0.001)
MOVE DISTANCE
STOP
ROTATE(90, DEGREES, CLOCKWISE)
DISTANCE = DISTANCE / 2
END WHILE
EXPLODE
END SUB

Where does the robot explode?

Update (23 Oct 2014):
Solution: Posted by me (Pratik Poddar) in comments!

### Social Network Friendship Paradox

Problem / Observation:

The friendship paradox is the phenomenon first observed by the sociologist Scott L. Feld in 1991 that most people have fewer friends than their friends have, on average. Prove it mathematically.

Update (23 Oct 2014):
Solution: Posted by Mike Earnest and Taz in comments!