3 Difficult Puzzles Involving Particles, String Loops & Pint Glasses
Can You Solve Them All?
Welcome to another round of Math Games. This time we will feature 3 difficult puzzles which require us to investigate the given situation. The first one is about particle collisions, the second one is about tying strings blindfolded, and the third one is about a very strategic pub game.
These puzzles are purely mathematical, but programming languages like Python are very useful tools for running simulations for these problems. So whether you are a pure mathematician or a computer scientist, there’s something for everyone!
Puzzle 1: Particle Collisions
There are subatomic particles trapped in a box. They can collide with one another but cannot escape from the box. The particles come in 3 species, call them A, B and C. When two particles of different species collide, they both change into the third remaining species. For example, when A collides with B, two C particles are produced.
Investigate. Specifically, analyze if the system will reach some form of equilibrium based on the given collision rules. Modular arithmetic may prove to be useful.
Note: There is no need to create a physically realistic simulation.
Puzzle 2: String Loops
In a big bowl, there are a number of strings all jumbled up. The strings are of the same length. You put on a blindfold and reach into the bowl of strings. You randomly choose two ends and tie them together. You repeat this process of tying two ends a number of times. You then remove your blindfold and find that some closed string loops have been formed.
Investigate. A good place to start would be to start with only 2 or 3 strings before scaling up.
Puzzle 3: A Pub Game
On a table in the Varsity pub, a number of empty pint glasses are placed in a circular arrangement. Each glass holds exactly a pint of liquid and the glasses are identical. Math students A and B play the following game.
A takes half a pint of water in a small glass (from the bar) and distributes the water amongst the pint glasses in any way they wish.
B then takes two adjacent pint glasses on the table, empties them (say, out the window) and puts them back into the circular arrangement.
A wants to make one of the glasses overflow, and B wants to prevent this.
Investigate. Again starting with a small number of pint glasses to get an idea of what’s going on would be advantageous.
Now send in your solutions to the following email to enter the arena, Challengers!
From now on, Challengers must send in their solutions to this email address.
Solutions can come in all forms of media:
a simple paragraph within the mail
a PDF
a Word document
screenshots of handwritten solutions
anything else that works
This means I will no longer allow comments on the Math Games puzzle post. But if you think I have made any mistakes on the questions, do feel free to reach out using either emails.
We want accuracy, speed and creativity. The more you excel in these criteria, the more you score ✨
A New Chapter of Math Games
New Rules, Better Scoring, A Bright Futuremedium.com
Now may the odds be ever in your favor 🏹
