Consider a 4×4 grid where each cell can be either selected or not selected. Two cells cannot both be selected if they share an edge (top, right, bottom, or left).
Read moreLife and Logic
Science, Future and controversy
Weekly Problem: The Grid
Weekly Problem- Let’s get complex
Consider this sequence:
1, 3, 7, 15, …
Each number seems to follow a simple rule, but there’s something magical happening when we look at their binary representations. This sequence demonstrates how simple patterns create complex constraints – a fundamental concept in complex systems.
Weekly Problem: The Card Sequence Problem
Problem Statement
You have three cards numbered 1, 2, and 3. You shuffle them and place them face down in a row.
Question: What is the probability that at least one card is in its correct position (i.e., card number matches its position)?
Read moreThe 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 start to wonder.
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).
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
Read moreWeekly 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
Read moreWeekly Problem: Number Theory
The Collatz Sequence Let’s explore one of the most deceptively simple yet unsolved problems in mathematics, first proposed by Lothar Collatz in 1937. The Rules Start with any positive integer n. At each step: If the number is even, divide
Read moreWeekly Problem: Fallacy Fallacy
Understanding the Fallacy Fallacy Test your knowledge about the fallacy fallacy – the mistake of assuming that if an argument contains a fallacy, its conclusion must be false.
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