Project Euler Forum

What does it mean "Denote by pn the place..." - does it mean that pn actually equals n?

$a_1,a_2,\dots,a_N$ will all appear in $C(10,12)$ somewhere, and not necessarily in that order. For example, it might be that $a_3$ appears first when you look at where each of the $a_i$ appear in $C(10,12).$ If that were the case, then $p_3 = 1$, since $a_3$ was first (and no, I've no idea if $p_3 = 1$, that's just an example).

So $p_n$ is the (1-based) order of $a_n$ in the list of all the $a_i$ when you arrange those in order by where they show up in $C(10,12).$

Isn't it true for C(3,2) that 0001021122 is lexicographically smaller than 0010211220 and meets the definition of C(k, n) given in the problem? I realize this is not a de Bruijn sequence, but the problem statement doesn't say that each combination must appear exactly once.

Consider all sequences of shortest possible length that contains every possible combination of the digits.
Denote by $C(k,n)$ the lexicographically smallest of these.

0001021122 does not contain "20".

yea, I was thinking 20 was included cyclically, but then of course there would be another 0 at the end and it wouldn't be the shortest sequence....thanks!