Problem
Find the number of permutations $(p_1,p_2,p_3,p_4,p_5,p_6)$ of $\{1,2,3,4,5,6\}$ such that for any $k$ such that $1 \le k \le 5,$ $(p_1,...,p_k)$ does not form a permutation of $\{1,2,....k\}$
My attempt
I have done a very ugly approach i.e doing case work and counting each case separately. After a long time after going through many mistakes,over countings, i have reached the correct answer $461$.
Initially, i have tried to come up with a recursive relation but i ended up missing too many cases.
Question
Since this an olympiad there must be a nicer and elegant solution. Can anybody share their insights to this problem? Thank you.
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