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The following pattern puzzle problem was given to me by one of my friend: $$\color{red}{5}$$ $$\color{blue}{24 \quad \quad \quad \text{M}}$$ $$\color{red}{4 \quad \quad \quad \quad \quad 6}$$ $$\color{blue}{40320 \quad \quad \quad 5040}$$ $$\color{red}{8 \quad \quad \quad 3}$$ $$\color{blue}{6}$$ $\color{blue}{\text{M}}=?$

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    $\begingroup$ Hi welcome to Puzzling SE! Can you provide the link to the site where you got it from if you didn't make the puzzle yourself? ;) $\endgroup$ – North Mar 5 at 5:03
  • $\begingroup$ @North actually one friend has given this problem to me in my whatsapp, so i don't know where he has got this problem; sorry for the inconvenience :( $\endgroup$ – Suresh Mar 5 at 5:07
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The numbers

In blue look like they ought to be the factorials of the number in red directly counterclockwise to it, with the exception of the red 6 and the blue 5040 = 7! I’d imagine either the 6 should be a 7 or the 5040 should be 720.

That said,

I’d hazard that the red 5 means the blue M should be 5! = 120.

Therefore

M = 120.

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