Numbers & Patterns
Mathematical marvels, statistical surprises, and numerical coincidences found in nature and human society.
Did You Know?
Every positive integer can be represented as the sum of at most three triangular numbers.
Proved by Gauss in 1796, this theorem shows how complex numbers can be built from simple geometric patterns....
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The Monty Hall Problem shows that switching doors triples your chances of winning.
This famous probability puzzle demonstrates how counterintuitive probability can be. Switching doors gives a 2/3 chance of winning,...
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The sum of the angles in a triangle is always 180 degrees, but only on a flat surface.
On curved surfaces like a sphere, triangles can have angle sums greater than 180 degrees. This demonstrates how...
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The largest known prime number has over 24 million digits.
Discovered in December 2018, this Mersenne prime is 2^82,589,933 - 1. If printed in standard font size, it...
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The game of Nim can be won every time using binary numbers.
This mathematical game can be solved completely using binary arithmetic. It's one of the first games to be...
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If you multiply 111,111,111 by itself, you get 12,345,678,987,654,321.
This palindromic pattern demonstrates how certain numbers can create symmetric results when multiplied. The result reads the same...
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The number 495 is the smallest number that can be arranged to make itself when its digits are each raised to their own power.
495 = 4^4 + 9^9 + 5^5. This property makes it a Münchausen number, demonstrating how numbers can...
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The probability of shuffling a deck into perfect order is 1 in 52 factorial.
This number is so large that if everyone on Earth shuffled a deck every second, it would take...
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There are exactly 6,670,903,752,021,072,936,960 possible sudoku grids.
This number was calculated in 2005 using computer analysis. It demonstrates how even simple-seeming puzzles can have enormous...