MHB What is the Correct Value of r if 9!/(9-r)! = 840?

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The equation 9!/(9 - r)! = 840 was analyzed to find the correct value of r. Initially, r was thought to be 4, but upon recalculating, it was determined that 9!/(5!) equals 3024, not 840. Consequently, there is no integer solution for r within the range of 0 to 9 that satisfies the equation. The discussion highlights the importance of careful calculation in solving factorial equations. Ultimately, the conclusion is that the equation has no valid solution.
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9!/(9 - r)! = 840

I found r to be 4.

Is this correct?
 
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RTCNTC said:
9!/(9 - r)! = 840

I found r to be 4.

Is this correct?

$\dfrac{9!}{(9-4)!} = \dfrac{9!}{5!} = 9 \cdot 8 \cdot 7 \cdot 6 = 3024$

there is no solution to the equation $\dfrac{9!}{(9-r)!} = 840$ for $0 \le r \le 9 \, , \, r \in \mathbb{Z}$
 
I messed up in my calculation. Thanks.
 

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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