MHB How Do You Calculate 'n' in This Permutation Problem?

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To find 'n' in the permutation problem, the equation 1/4! + 1/5! + 1/6! = n/7! is solved by multiplying both sides by 7!. This leads to the calculation of n as 7 * 6 * 5 + 7 * 6 + 7, resulting in n = 259. The discussion suggests that the number 259 might hold a special significance, possibly as an encrypted message. The problem is deemed solvable and not impossible.
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Find 'n' using permutations:

1/4! + 1/5! + 1/6! = n/7!
 
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Arunachaleshwar said:
1/4! + 1/5! + 1/6! = n/7!

Welcome on MHB Arunachaleshwar!...

... the problem You propose is not 'impossible'... multiplying the two sides for 7! You have...

$\displaystyle n= 7 \cdot 6 \cdot 5 + 7 \cdot 6 + 7 = 259$

... can it be that You are sending an encrypted message in which the number 259 has a special meaning? ...

Kind regards

$\chi$ $\sigma$
 

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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