Category: mathematics
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The Equivalence of Legal Argumentation and Mathematical Proof: Why Precedent and Proof by Analogy Are the Same Thing
The Basic Structure of Legal Precedent In legal argumentation, lawyers constantly use this reasoning: In case Y, the situation was such-and-such, and the defendant was acquitted. In our current case X, the situation is like the situation in case Y. Therefore, the same argumentation that led to acquittal in case Y should apply, and the…
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Weekly Problem: Guinea Pig Fur Color Genetics
The Problem In a laboratory study, scientists are breeding guinea pigs to understand the genetics of fur color. They observe an interesting pattern: When two black guinea pigs mate, about 3/4 of their offspring are black, while 1/4 are white.When two white guinea pigs mate, ALL of their offspring are white.When a black guinea pig…
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Weekly Problem: The Game Show Dilemma
The problem Imagine you’re a contestant on a popular game show. The host shows you three closed doors: behind one is a brand-new luxury car, and behind the other two are goats (which, unless you’re in the market for a goat, are considerably less valuable prizes). You select Door #1, hoping it contains the car.…
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Weekly Problem: Arithmetization
🔢 Arithmetization: Encoding Logic as Numbers Transform mathematical formulas into unique numbers using Gödel numbering 1 Enter a Formula ℹ️ What is Arithmetization? Arithmetization is a technique that assigns unique numbers to mathematical symbols and formulas. This allows us to treat statements about mathematics as mathematical objects themselves! This concept is crucial in proving Gödel’s…
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Weekly Problem: The Grid
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).
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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.
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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)?
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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: 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 it by 2 If the number is odd, multiply it by 3 and add 1…
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Weekly 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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Weekly Problem: Geometric Maze Optimization
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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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The Pizza Theorem. Weekly Problem no. 8
The Pizza Theorem Challenge by Yildiz Culcu Rotate Cuts Show/Hide Solution Problem: A pizza is cut by 8 straight lines through a point P, which is not at the center of the pizza. The cuts are made at equal angles (45° apart). Prove that the sum of the areas of alternate pieces is equal. Questions…