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 works a little on his 15s puzzle redo that he started in his previous live session: https://www.youtube.com/watch?v=ixkLFYcb0T0 and programs a math/logic puzzle, checking whether the statement “Every card with a T on one side has a 3 on the other” is true or false. The original puzzle comes from an old video by James Grime, recorded before Simon was born (the fact that Simon finds particularly funny):
This is Simon’s remix of a video by James Grime about the same subject on the SingingBanana math channel: https://www.youtube.com/watch?v=ODtwehGzoLM
The Utilities Problem is a problem about connecting three houses to three utility companies of which every company provides three services (water, gas, electricity) so that no lines cross.
Simon proves the problem impossible by contradiction (by assuming it’s possible and applying Euler’s Formula about 3D Solids to the solution).
Prime Number Theorem
An interesting sequence that correlates with a chessboard game and golden ratio
Imperial system of measurements
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?
Answer: yes. Here Simon explains why:
Simon has been studying the differences between a catenary (the curve a free hanging chain makes) and a parabola (the trajectory of a thrown ball), via the SingingBanana math channel. He told me a lot of interesting facts about the catenary:
- it’s the fastest track for any round object to roll to any point on a curve;
- when you roll two balls on a catenary at different heights, they will crash exactly in the middle;
- when turned upside down, a catenary makes the strongest bridge;
Another paper dodecahedron, now a pop-up one! The idea comes from an old video on the SingingBanana math channel.
Simon learned this from the SingingBanana channel:
In this video, Simon solves the famous Motorway Problem (or Steiner Problem) naturally, using soapy liquid. The problem is about four towns located in a one mile squared and looking for the shortest and most efficient way to connect them. Simon goes through the possibilities and then uses his homemade prop to find the shortest path to connect four points. Sometimes, the prop manages to show the local minimum instead of the solution, Simon explained, so make sure you get rid of the extra bubbles and pull the prop from the water vertically, not horizontally.
Simon also explains the physics behind the experiment: The trick works because a bubble minimises its tension.
Simon shows a very special kind of magic square in which not only the rows, the columns and the diagonals add up to the magic number but also “plus signs”, crosses, sums of diagonals – all in all, thousands of ways to make the magic number (especially if you wrap the grid around a torus). Simon also explains the equation behind the magic!
Simon learned about the equation and the way to make the square from a comment to this video on the SingingBanana channel.