This blog is about Simon, a young gifted mathematician and programmer, who had to move from Amsterdam to Antwerp to be able to study at the level that fits his talent, i.e. homeschool.

Never a dull moment sitting down at a summertime terrace together with Simon. Just had a swim at the local pool and thought he was tired, but there he goes: Mom, I’ve got a game for you. Made these 9 cards and taught me how to play: each player grabs one card at a time and whoever has accumulated a valid sum or a set of three operators has won.

It was later that he showed me that the game is actually a number variant of tic tac toe and one should use the same strategy to get three in a row:

This is a Japanese version of the famous River Crossings Puzzle that Simon learned from the Scam School channel (yes, our little programming and math nerd actually watches Scam School, a channel dedicated to social engineering at the bar and in the street!)

The answer, a sequence of 17 moves:

Simon showing the classic River Crossings puzzle to friends

Math graphs for solving the simple and the more advanced River Crossings puzzles using minimum vertex covers and Alcuin Numbers (learned via Numberphile):

Simon has invented this card trick using a random field of cards and allowing him to predict nearly the whole path through the field. You can play along as a viewer and see how Simon will nearly guess your card (the card that your finger will end up on at the end of the trick), narrowing his final guess down to just a couple of cards (three in this case).

This trick is a version of Kruscal Count. Simon learned about random fields and Kruscal Count from a video by James Grime on the Singing Banana channel.

In this live session, Simon continue my 15s puzzle redo live session (“yet again, but I swear this is going to be the last time I do this!” Simon said). Here’s a link to the previous part. This week’s live stream went great, Simon kept it concise, didn’t panic while debugging, largely thanks to a wonderful supportive audience. And he even got some interesting personal questions asked in the end!

Simon has developed his version of the Magic Cards, this time in Base 3. He invented this system completely on his own and actually created a program in Processing (Java), using ternary function, to make the cards! The the code for creating the five cards in Processing and exporting the images as png files is available on Simon’s page on GitHub: https://github.com/simon-tiger/browns-criterion-base3

To play the game, have someone think of a number between 0 and 242 and let that person look for his/her number on every card and tell you which colour it is on every card. Every card stands for a power of 3: 81, 27, 9, 3, and 1. There are three grids of numbers on every card, a blue grid (representing the zeros in base 3), a red grid (representing the ones in base 3), and a green grid (representing the twos in base 3). After your friend has found his/her number on all the five cards, you can go ahead and add all the results up to guess the number. Alternatively, if you find working with base 3 too difficult, just sum up all the red numbers in the top left corners (on all the cards where your friend’s number was red), then double all the red numbers in the top left corners (on all the cards where your friend’s number was green) and add all of those together to guess the number.

Simon started out by actually trying to draw the magic cards:

But quickly realised he’s better off writing a computer program to fill in the grids. When the program (pretty tough to write) was finally ready, he tried to print a card out and… ran out of ink on our home printer. Next, we rushed to the print shop, as it was about to close.

“Mom, I can calculate why it says 17 million colours! It’s 256 cubed!” (255 for Red, Green and Blue plus one for alpha).

Here is another interesting puzzle Simon learned from the SingingBanana math channel, about two drugs undergoing testing in the course of two days. The fish drug cured 63 out of 90 people (70%) on the first day and 4 out of 10 people (40%) on the second day. The second drug cured 8 out of 10 people (80%) on the first day and 45 out of 90 people (50%) on the second day. Which drug is more efficient?

Simon has crafted a nice game today, inspired by a video in which mathematician Katie Steckles shows several mathematical games. Simon wasn’t sure what the game was called so he named it “Reds and Greens”. The objective of the game is to accumulate a set of three cards sharing the same property (such as the same number of green dots or red dots, the same total number of reds and greens or a set in which all the three possible variants – one, two and three dots of the same color – would be present). Each player pulls a card from the stack (all the cards are lying face up) and the one who collects a set first wins. Simon has actually programmed the cards in Processing (Java) – quite a strenuous task. Below is the jpeg pic of what he made and his code in Processing.

Simon also explained how the game is very similar to Tic Tac Toe, look at the photo below and you’ll see why:

Simon talking about his Tantrix Game code and the math behind it. It has been Simon’s first community project, many thanks to everyone who has contributed hexagonal tiles for the game! The game isn’t finished yet, but the video gives a good insight into the work in progress. Simon will finish it at a later date he says. Feel free to try and finish it on your own and share your results! The code is on GitHub at: https://github.com/simon-tiger/tantrix

Today is one of the most beautiful days in Simon’s life: NYU Associate Professor and the creator of Coding Train Daniel Shiffman has been Simon’s guarding angel, role model and source of all the knowledge Simon has accumulated so far (in programming, math, community ethics and English), and today Simon got to meet him for the first time in real life!