For a positive integer $n$ define $T(n)$ to be the number of strictly larger integers which can be formed by permuting the digits of $n$.
Leading zeros are not allowed and so for $n = 2302$ the total list of permutations would be:
$2023,2032,2203,2230,\mathbf{2302},2320,3022,32 02,3220$
giving $T(2302)=4$.
Further define $S(k)$ to be the sum of $T(n)$ for all $k$-digit numbers $n$. You are given $S(3) = 1701$.
Find $S(12)$.
Solution
No solution yet. Write yours at
solutions/s862.md.