Tag: Mathematics
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The 3-Sum Puzzle
What’s This All About? Imagine you’re given a list of numbers. Let’s say 20 numbers, chosen from 1 to 100. The question is simple: Is it always true that you can find three different numbers in the list whose sum is divisible by 3? It sounds easy, right? But once you try different lists, you’ll…
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Solution to The Happy Ending Problem
What’s This All About? Imagine playing a game where you put dots on a piece of paper. The challenge is to find dots that can be connected to make different shapes. But there’s a catch – the shapes need to be “convex” (no dents or inward angles).
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The Happy Ending Problem
Points, Patterns, and a Mathematical Love Story In 1933, a young mathematician named Esther Klein noticed something interesting about points on a plane. This observation led to a famous problem – and eventually to her marriage to another mathematician, George Szekeres. Hence, this became known as the “Happy Ending Problem”! This Week’s Challenge Basic Concept:…
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Weekly Problem Fermat’s Last Theorem
Fermat’s Last Theorem: The Most Famous Problem in Number Theory “I have discovered a truly remarkable proof which this margin is too small to contain.” – Pierre de Fermat, around 1637 The Statement For any integer n > 2, there are no positive integers x, y, and z that satisfy: xⁿ + yⁿ = zⁿ…
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Weekly Problem no.14: Beethoven’s 5th!
Cryptophonic Challenge: Beethoven’s Victory Code The Cryptophonic Challenge: Beethoven’s Victory Code Click to Start Audio Engine 🎵 Decode the Victory Symphony Level: 1/3 Current Mission: Decode the famous rhythm that became a symbol of victory… Attempts remaining: 3 30s lockout remaining Pattern 1: • • • ― ❔ Pattern 2: ― • • • 🔒…
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Weekly Problem no.13 Vector Chase!
Here’s our weekly mathematical problem. this time in Geometry!
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Napoleon’s Theorem
weekly Problem no.5 in two difficulties One of the most elegant results in geometry began with a surprising observation about triangles. Take any triangle – it doesn’t matter what shape or size – and build equilateral triangles on each of its sides (pointing outward). Now find the centers of these three equilateral triangles. When you…
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Problem #2 The Rendezvous Problem
The Rendezvous Problem in Game Theory 07/10/2023 The Rendezvous Problem is a fascinating dilemma in game theory that explores decision-making in uncertain situations. Imagine this scenario: Two friends, Alice and Bob, have agreed to meet in a large park they’ve never visited before. Upon arrival, they realize the park is much bigger than expected, making…
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Problem 1: The Traveling Salesperson problem 10/01/2024
And here the solution to our Problem #1 04/10/2024 As PNG and HTML file See more on the weekly Problems Page.
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Decision Theory and the Power of Counterfactuals
A Research team on Spotify develops a new ML model for decision-making using counterfactuals. Why that’s exciting! Self-driving cars, medical diagnosis, investment plans, and game theory are all applications of decision-making AI. Decision theory is the study of algorithms for correct decisions, but it comes with a few obstacles. Making the right decision is quite…