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Given a group of $n$ ($n \in N$) people, find

  1. the number of non-leaders $a_0$ ($a_0 \in N$ and $a_0 \leq n$) and
  2. the number of leader levels $K$ ($K \in N \cup \left{0\right}$)

as functions of $n$ such that

$$ a_0 + \left \lceil 10^{-1} a_0 \right \rceil + \left \lceil 10^{-1} \left \lceil 10^{-1} a_0 \right \rceil \right \rceil + \cdots + \overbrace{\left \lceil 10^{-1} \left \lceil 10^{-1} \cdots \left \lceil 10^{-1} a_0 \right \rceil \cdots \right \rceil \right \rceil}^{K \text{ layers of } \left \lceil ~ \right \rceil} = n~, $$

and

$$ 1 \leq \overbrace{\left \lceil 10^{-1} \left \lceil 10^{-1} \cdots \left \lceil 10^{-1} a_0 \right \rceil \cdots \right \rceil \right \rceil}^{K \text{ layers of } \left \lceil ~ \right \rceil}< 10~. $$

Posted Sat Apr 9 19:42:40 2022

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