art, Crafty, Geometry Joys, Math and Computer Science Everywhere, Math Riddles, Murderous Maths, Notes on everyday life, Simon makes gamez, Simon teaching, Simon's sketch book, Together with sis

Math puzzles: Is it Possible?

Simon has been fascinated by these possible-impossible puzzles (that he picked up from the MajorPrep channel) for a couple of days. He prepared many paper visuals so that Dad and I could try solving them. This morning he produced this beautiful piece of design:

Simon showing one of the puzzles to another parent while waiting for Neva during her hockey training
Simon’s original drawing of the doors puzzle. The solution of the puzzle is based on graph theory and the Eulerian trail rule that the number of nodes with an odd degree should be either 0 or 2 to be able to draw a shape without lifting your pencil. The number of rooms with an odd number of doors in the puzzle is 4 (including the space surrounding the rectangle), that’s why it’s impossible to close all the doors by walking though each of them only once.
Simon explaining odd degree nodes
Murderous Maths, Simon teaching, Simon's sketch book

Larger than Graham’s number!

Simon explains strong and weak tree sequences and reveals the greatest finite number used in mathematics: TREE(3), a lot larger than Graham’s number. The TREE sequence is a fast-growing function arising out of graph theory.

Simon comments: “What is you make TREE(TREE(3))?”

Inspired by:
http://googology.wikia.com/wiki/TREE_sequence 
https://www.youtube.com/watch?v=3P6DWAwwViU