View source for Why Dinning Philosopher problem requires at least five participants?

In the famous Dinning Philosopher problem, it is standard to start with at least five participants. The reason is obvious that any number below this, will have trivial behavior. However, there was rarely a document that I have found on the web that directly answers why this is the case.

=The Quintic Formula=
It is until I saw the explanations<ref>{{:Video/Why There's 'No' Quintic Formula (without Galois theory)}}</ref><ref>{{:Video/The Insolvability of the Quintic}}</ref><ref>{{:Video/Why can't you solve quintic equations? - Galois theory explained intuitively}}</ref> of why there are no solutions for Quintic Formula, that finally gave me the convincing argument. It has to do with the infinite combinatorial possibilities generator by five [[commutator]]s.

<noinclude>
{{PagePostfix
|category_csd=Galois theory,Quintic Equations,Symmetry,Commutator,Permutation
}}
</noinclude>