Today, another problem from Math Horizons.
The following figure illustrates a Sierpiński carpet, a fractal structure. We start with a square of side length equal to 1 unit length. At each iteration, one cuts a square into 9 subsquares and deletes the middle square. In the limit, this will be a Sierpiński carpet.
Two questions:
- How many squares remain at each iteration?
- An ant, located at one corner of the carpet wants to travel as fast as possible to the diagonally opposite corner without falling into a hole. She can travel in any direction for that. She can do better than a distance of two unit lengths (simply following the outer edges). What is the shortest distance she can cover?
Previous iteration: #751726 (the answer I had was indeed by letting the bulb become warm, but I appreciate the other even more creative solutions to think out of the box)
