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title JOC

Topics to be discussed

2/3rds average problem:

This is a game where a bunch of people are expected to propose a number between 0 to 100 and the winner is someone whose number is closest to 2/3rds of the average of all the numbers proposed. We need to create a functional google sheet for this. Atharva's point is to keep the google form open in its editable version. We can display the output on the google sheet. We need to create this google form. The game is played for some time and we teach students on the concept of Nash equilibrium. The inutitive idea should be enough without any rigorous proof.

Birthday Paradox:

  1. We ask everyone to enter their day and month over a google form. It is good to capture this information by giving htem a dropdown menu. Otherwise, they tend to input in a not so readable format. After this, we will display all the information in a random order in a google sheet and then ask them if they are able to see any collisions. This is just to make it fun and keep them engaged. There can be a hidden sheet, which has the entries in the ascending oder.

  2. We then discuss the fact that the collisions are common. We write a code to illustrate this in google sheet itself.

  3. We will now propose the mobile phone storing problem. Where 100 mobile phones are stored in a 10x10 grid. We will ask them to calculate the probability of a collision. Rather, show this by writing a code in python.

  4. We then check this result for 1000, 10000, 100000, 1000000 mobile phones and so on.

  5. Motivate the idea of storage where storage, retrival and lookup can all be done in almost constant time.

  6. We will conclude with the idea of hashing and introduce some of its variants (if the audience are up to it).

Greedy Pig

Greedy Pig Atharva brought this to our notice. This seems to be an amazing exercise for students to play and figure out what is happening. We can create a google form for this? We will play this a couple of times to understand what script will make it interesting.

Online Hiring

The story of e (the derivation of the value and compound interest)

Dart Problem

Same underlying concept as the Greedy Pig. Can be left as an exercise for the students.

The German Tank Problem

Same underlying concept as the Greedy Pig. Can be left as an exercise for the students.

Vigenere Cryptanalysis

Sensex Prediction

Baysian Learning

Shakuni Problem and Prime Factoring

Halting Problem

Solve the first few Python Oceanverse Questions

This is useful for beginners to get started with python.

Pagerank

Compression and Entropy

Binary Search

Laptop thief, Curse on your bank account, Imposition with ctrl cv, dictionary example, finding sqrt of 11.

Gradient Descent using the subjects example.

Interesting Problems that don't overlap with JOC.

Catalan Numbers

Catalan Numbers

  • Problems:
  1. Paths that don't cross the diagonal.
  2. Number of Dyck words.
  3. Number of ways to triangulate a polygon.
  4. Number of binary search trees with n leaf nodes.
  5. Number of ways to parenthesize an expression.

Error Correcting Codes

  1. Hamming Codes
  2. Solomon Reed Codes (Using Lagrange Interpolation)

Anomaly Detection