Crafty, Math and Computer Science Everywhere, Math Riddles, motor skills, Murderous Maths, Simon makes gamez, Simon teaching, Simon's sketch book

Proof Visualization. Warning: Mind-boggling!

Inspired by the Card Flipping Proof by Numberphile, Simon created his own version of this proof. He made a solitaire game and proved why it would be impossible to solve with an even number of orange-side-up circles. He drew all the shapes in Microsoft Paint, printed them out and spent something like two hours cutting them out, but it was worth it!

The colourful pieces in the lower row are a “key” to solve the solitaire puzzle. The objective is to remove all the circles. One can only remove a circle if it’s orange side up. Once a circle is removed, its neighbouring circles have to be flipped. Using the key, start with the yellow pieces, and move in the direction of the “grater than” sign (from smallest to largest).

If there’s an odd number of orange circles in the middle, then the end pieces are the same, both orange or both white. In both cases the total number of orange circles will also be odd. If there’s an even number of orange circles in the middle, then the ends have to be different (one orange, one white).

In the case of odd number of orange pieces, the ends have to match. In the case of an even number of orange pieces, you would have pieces that point the same way at both ends. “Now we’ve proven that to make this puzzle possible it has to have an odd number of orange pieces”, Simon says.

Why? Imagine a stick figure that always walks to the right, but always faces in the direction of the arrow (as in it can’t go backwards). It would flip every time it reaches an orange circle. Focusing on everything except the ends, if there are an odd number of orange circles, the puzzle pieces would face the other way. Which means that the end pieces are the same, and therefore the end circles are the same. If there are an even number of orange circles in the middle, the puzzle pieces would face the same way. Which means that the end pieces are different, and therefore the end circles are different.

Simon finds this sort of proof easy, but I felt like my brains are going to boil and dripple through my ears and nostrils. He patently exlained it to me several times and types the above explanation, too.

Crafty, Math and Computer Science Everywhere, Notes on everyday life, Simon makes gamez, Simon's sketch book, Together with sis

Sinterklaas math game with “gingerbread buttons”

It’s Sinterklaas season in the Dutch-speaking world and, of course, as we have started baking the traditional spiced cookies called kruidnoten (“gingerbread buttons”) Simon didn’t want to miss an opportunity to play a version of peg solitaire with eatable pieces!

Simon has baked these himself (together with Neva)
the winning strategy
Simon mixing the right proportion of spices, grinding clove (then adding nutmeg, white pepper, ginger, cardamom and cinnamon)
Computer Science, Crafty, Logic, Simon's sketch book

Simon crafting a search engine with sticky notes

Simon working on a simplified version of a search engine, including just a few documents, and performing calculations to determine how many searches one should do to make creating an index of all the documents efficient (something he has picked up in Brilliant.org’s Computer Science course.

screenshot from Brilliant.org’s Computer Science course
Crafty, Math Riddles, Math Tricks, Murderous Maths, Simon's sketch book, Together with sis

More Puzzles from Maths Is Fun

In an earlier post, I have mentioned that for many games he programs Simon got his inspiration from the site Maths Is Fun. Perhaps I should add that at our home, Maths Is Fun has become an endless source of fun word problems, too! The problem below has been our favourite this week:

Simon’s equations to solve the problem
Simon has developed a system to show the relation between the actual time a and time m that a mirrored clock would show: m = 12 – a
Another clock puzzle from Maths Is Fun
Simon’s solution
solving this during his evening tea

Some of the puzzles Simon likes to recreate with paper and scissors rather than program:

A version of Connect 4 but this time with the tables of multiplication! Every player is only allowed to move one paper triangle at a time (the triangles indicate which two numbers one can use to get the next product in the table). The one who colours four products in a row wins.
As the game progresses it gets trickier
For the jug puzzle game, Simon has developed a graph plotting the winning strategy (analogous to what he once saw Mathologer do for another game).
Double-sided numbers, sort of a two-dimensional cellular automaton. The objective is to get to a state when all the numbers would be one colour. The rule: if a cell changes its colour, its four neighbours (not diagonal) also change colour. There’re also other versions of this puzzle with more difficult initial conditions.
A number-guessing game based on binary representation. When he was 8 years old, Simon programmed a similar trick in Processing. He also developed the same sort of trick for base 3 numbers.

Simon and Neva have also especially liked the Tricky Puzzles section (puzzles containing jokes).

Crafty, Electricity, Electronics, Engineering, Experiments, Geometry Joys, Notes on everyday life, Physics, Simon teaching, Together with sis

Vanishing Letters

Simon’s way to celebrate Helloween: a little demo about how red marker reflects red LED light and becomes invisible. A nice trick in the dark!

We also had so much fun with the blue LED lamp a couple days ago when Simon discovered that it projects perfect conic sections on the wall! Depending on the angle at which he was holding the lamp, he got a circle, an ellipse, a hyperbola and a parabola! Originally just a spheric light source we grabbed after the power went out in the bathroom, in Simon’s hands the lamp has become an inspiring science demo tool.

Crafty, Experiments, motor skills, Physics, Together with sis

Some Physics Demos with Geomag

Rotating a merry-go-round with a “magic wand”
One beautiful thing about Simon’s recent return to Geomag is that, as it turned out, he is now capable of building all the tricky constructions on his own, without any help from the grown-ups
An example of a Gaussian Gun, a magnetic chain reaction to launch a steel ball at high speed. As soon as the rolling ball hits the magnet, another ball in the opposite side is launched.
Crafty, Geometry Joys, Good Reads, Logic, Murderous Maths, Simon teaching, Simon's sketch book

Attractiveness vs. Personality

Debunking the stereotype that all attractive guys/girls are mean, something Simon has learned from MajorPrep and the How Not to Be Wrong book by Jordan Ellenberg. The slope in dark blue pen shows our scope of attention, a pretty narrow part of the actually diverse field of choices.
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
Computer Science, Crafty, Electronics, Engineering, Good Reads, Milestones, Simon's sketch book

Simon trying to build a 8-bit computer in circuit simulators

As some of you may know, Simon is working on building a real-life 8-bit computer from scratch, guided by Ben Eater’s tutorials (it’s a huge project that may takes months). He has also been enchanted by the idea to build the computer in a simulator as well, researching all virtual environments possible. The best simulator Simon has tried so far has been Circuitverse.org, although he did stumble upon a stack overflow error once, approximately half-way through (maybe the memory wasn’t big enough for such an elaborate circuit, Simon said). You can view Simon’s projects on Circuitverse here: https://circuitverse.org/users/7241

Link to the project that ended up having a stack overflow: https://circuitverse.org/users/7241/projects/21712

And here is a link to Simon’s new and more successful attempt to put together a SAP-1 (simple as possible) processor (work in progress), something he has been reading about in his new favourite book, the Digital Computer Electronics eBook (third edition): https://circuitverse.org/users/7241/projects/22541

https://circuitverse.org/users/7241/projects/21712
the register
the RAM
https://circuitverse.org/users/7241/projects/22541

Simon has also tried building an 8-bit computer in Simulator.io, but it was really difficult and time consuming:

Version in simulator.io

The next hopeful candidate was the Virtual Breadboard desktop app for pc. Simon downloaded it about ten times from the Microsoft store but it somehow never arrived, most probably because our Windows version was slightly outdated but who knows.

And finally, Simon has also discovered Fritzing.org, an environment for creating your own pcbs with a real-life look. He may attempt actually making a hardcopy SAP-1 via Fritzing after he’s done with the Ben Eater project. Conclusion: sticking with Circuitverse for the time being.