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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
Math Riddles, Murderous Maths, Simon's sketch book

A quiz full of fun tricks

Simon got these from the Scam School channel.

I first only got a strip paper with a sequence of green sticks written on it, separated by comas. Simon did tell me those were pieces of numbers, the way they appear on a calculator screen, and that I was supposed to comolete the sequence. I tried to give this one a shot. To stop the waiting that began to seem eternal he eventually gave me the answer: the green sticks were everything BUT the numbers! Below you see the competed version:

Here, too, one is supposed to continue the sequence of numbers written in a column. You see the pattern?

Here too, come up with the next character:

See the pattern now?

The next one is hilarious! Rearrange the letters below to write ONE WORD:

And in the last puzzle, the nine words used to have something in common, but now it’s just eight of them.

If you get stuck with any of these, leave a plea for help in the comments!

Math Riddles, motor skills, Murderous Maths

Archemedes Puzzle

Simon showing the Archimedes puzzle he made himself to his Russian grandmom. Archimedes had created a colorless version of this puzzle, but Simon decided to add colors and use the Four Color Theorem (stating that any map is possible to color with four or fewer colors without two identical colors being adjacent) to help himself solve this murderously challenging puzzle.