Question 35
The number $695$ is to be written with a factorial base of numeration, that is, $$
\begin{aligned} 695={}&a_1+a_2\cdot2!+a_3\cdot3!\\ &+\cdots+a_n\cdot n!, \end{aligned}
$$ where $a_1,$ $a_2,$ $a_3,$ $\ldots,$ $a_n$ are integers such that $0\le a_k\le k,$ and $n!$ means $n(n-1)(n-2)\cdots2\cdot1.$ Find $a_4.$
\begin{aligned} 695={}&a_1+a_2\cdot2!+a_3\cdot3!\\ &+\cdots+a_n\cdot n!, \end{aligned}
$$ where $a_1,$ $a_2,$ $a_3,$ $\ldots,$ $a_n$ are integers such that $0\le a_k\le k,$ and $n!$ means $n(n-1)(n-2)\cdots2\cdot1.$ Find $a_4.$