what a deranged number!!

[ianmii]

As usual, another super wonderful math video!!! Also I Love your shirt!!! 🥰

[marcelob.]

Deja vu or my other self in a parallel universe have already watched this video? I wish I can ask him but we still can't communicate.

[ambidexter]

1854 is possibly the birth year of Sherlock Holmes.

[maestrobrutalizador]

This is unnecessarily complicate: its far easier to reason as follows. If d_k is the number of derangements in k persons then n!= sum(C^n_k d_k, k=0 to n) as every permutation have exactly 0, 1, ..., or n fixed points where C^n_k is the binomial number n over k. Now, its easy to show using formal series that for any sequence {a_k}_k it follows that b_n=sum( C^n_k a_k, k=0 to n) if and only if a_n=sum(C^n_k b_k (-1)^k, k=0 to n), so it follows in our case that d_n=sum(C^n_k k! (-1)^k, k=0 to n), and using the series of the exponential function this last result can be simplified to d_n=floor(1/2+n!/e). 😁

[Blingsss]

Deranged? More like mathematically misunderstood! Numbers like this are a reminder that math has a sense of humor.This video makes me want to brush up on my skills. SolutionInn has been my go to for tackling these unexpected surprises.

[notfancy]

!N ~ N!/e would have been a nice observation for closing 😊

[alex_ramjiawan]

What about the integral formula or using the nearest integer of n!/e?