Understanding Factorials: A Combinatorics Primer

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Factorials are defined such that n! = n * (n-1)!. The equation n! - (n-1)! simplifies to (n-1) * (n-1)!, indicating a misunderstanding in the original book's statement. The correct interpretation shows that n! - (n-1)! equals (n-1) * (n-1)!, not (n-1)! * (n-1)!. This highlights the importance of accurately applying factorial rules in combinatorial mathematics. Understanding these principles is crucial for mastering combinatorics concepts.
Takuya
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In my combinatorics book, it's discussing inclusion-exclusion, and it says that n!-(n-1)! = (n-1)!*(n-1)!

Can someone help me understand the rules of factorials? Thanks!
 
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The book has a mistake:

n! - (n-1)! = n * (n-1)! - (n-1)! = n * (n-1)! - 1 * (n-1)! = (n-1) * (n-1)!
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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