After a whole night working on my writing and not feeling very fresh in the morning, I told Simon about the three ages of life: the young age is when one can party all night long and the next morning feel like one has been sleeping like a rose, the middle age is when one parties all night long and the next morning feels like one had been partying all night long, and the old age is when has been sleeping all night long and the next morning feels like one has been partying all night long. He immediately drew these pictures, telling me it’s just like 1-input 1-output logic gates, but the only one that makes sense is the OR.
Simon is doing an increasing load of Brilliant’s daily challenges.
Some more recent challenges:
Three boxes with fruit, all the three labels are misplaced. What is the minimum number of times one will have to sample a random piece of fruit from one of the boxes to know how to label all the three boxes correctly? From Mind Your Decisions.
Connect A and A’, B and B’, C and C’, D and D’ so that no lines intersect. (Neva added colors).
Dividing 11 coins among three people: “How many ways can you divide 11 coins to 3 people? How many ways are there if each person has to get at least 1 coin?” From Mind Your Decisions.
Solving a simple quadratic equation geometrically: the geometric interpretation of “completing the square”, a notion from deriving the quadratic formula. From Mind Your Decisions.
Which way do the arrows point? (Simon made this drawing in Microsoft Paint):
How many times, on average, do you have to roll a dice until you get a repeated value? I saw this probability challenge on the Mind Your Decisions channel. I decided to test it experimentally. First, I repeated the experiment myself in two sets of 50. Then I created a diagram in the Wolfram Language to visualize the distribution. Finally, I made a p5.js sketch to roll the dice thousands of times.
Link to my code: https://editor.p5js.org/simontiger/sketches/gM0xws9D
Link to my Wolfram Notebook: https://www.wolframcloud.com/obj/620bf4df-077f-4ce8-8210-c06037f58f9b
In a complete binary tree, every node has two children (except for the bottom nodes that don’t have any children at all). This means one mind-blowing thing: that the bottom row always has more nodes than the number of nodes in the entire rest of the tree! Example: if there’s one node at the top of the tree, two nodes in the second row, four nodes in the third row and eight nodes in the bottom row, the bottom row has more nodes (8) than the remaining part of tree (7). I’ve been thinking about this, and I applied this to the real world:
The average number of children a parent has in the world is 2.23 (I’ve used an arithmetic mean, which is oversimplistic, should have probably used the harmonic mean). Does this mean that currently, the number of children exceeds the number of parents? The definition of “children” I’m using are people who don’t have children, so the last row of nodes so to speak. By “parents” I’m counting all generations. If you just want to talk about now, the parents living now, then you have to trim the top rows (the already dead generations). If the average number of children is 2 or more, are there going to be more children in the world than parents?
Well, in this model, I’m ignoring crossover. This means we should consider every node in our tree for 2 people*. So, now, if the average number of children is 4 or more, there’re going to be more children than parents. So, what I said earlier was wrong. The average number of people doesn’t exceed 4, so there aren’t more children than parents. But the number of children today may still exceed the number of parent generations still alive.
Simon prepared this project as a community contribution for The Coding Train (Simon came up with his own way to draw the Hilbert Curve and added interactive elements to enable the user to create other colourful space-filling curves (Hilbert Curve, Z-order Curve, Peano Curve and more!). You can see Daniel Shiffman’s Hilbert Curve tutorial and coding challenge on The Coding Train’s website (including a link to Simon’s contribution) via this link: https://thecodingtrain.com/CodingInTheCabana/003-hilbert-curve.html
Interactive full-screen version, allowing you to change the seed and the grid size: https://editor.p5js.org/simontiger/full/2CrT12N4
Simon’s latest independent coding project involved some biology lessons! He loves the channel Primer by Justin Helps and watched his evolution series many times, studying the rules for species’ survival and multiplication. This resulted in two interactive evolution simulations, in both of which Simon recreated the rules he learned. The first simulation doesn’t involve natural selection and is based on these two videos: Simulating Competition and Logistic Growth and Mutations and the First Replicators.
Full Screen interactive version: https://editor.p5js.org/simontiger/present/MK4b75542
Simon added natural selection in Part 2, based on Primer’s video Simulating Natural Selection (the code Simon wrote from scratch):
Full Screen interactive version: https://editor.p5js.org/simontiger/present/68WXliTza
For over a month, Simon has been fascinated by Presh Talwalkar’s channel Mind Your Decisions. The channel is full of short videos on famous math problems, logic riddles, proofs and mental math tricks. Simon has also ordered a compilation of Talwalkar’s five most interesting books, including “The Joy of Game Theory: An Introduction to Strategic Thinking”, that we are currently very much enjoying together, and four more, that Simon is reading on his own: “40 Paradoxes in Logic, Probability, and Game Theory”, “The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias”, “The Best Mental Math Tricks”, and “Multiply Numbers By Drawing Lines”.
This one became Simon’s favourite brain teaser. It sounds like it’s filled with irrelevant information, but somewhat counterintuitively, every little bit of information in this puzzle helps! Here is the puzzle: A mathematician tells a census taker he has 3 children. The product of their ages is 72 and the sum of their ages is the house number. The census taker tries to figure it out but explains he still does not know. The mathematician says, “Of course not. I forgot to tell you my oldest child loves chocolate chip cookies.” Now the census taker figures it out. What are the ages of the children?
Simon has also picked up many nifty tricks and beautiful magic squares, both from the book and from the YouTube channel.
Multiplication by drawing lines has been a huge hit, Simon has also taught this method to his sister and a friend in Amsterdam:
Simon learned this from an alternating series visualization by Think Twice.