Pandigital multiples
Take the number \( 192 \) and multiply it by each of \( 1 \), \( 2 \), and \( 3 \):
\[ \begin{align} 192 × 1 = 192\\ 192 × 2 = 384\\ 192 × 3 = 576\end{align} \]
By concatenating each product we get the \( 1 \) to \( 9 \) pandigital, \( 192384576 \). We will call \( 192384576 \) the concatenated product of \( 192 \) and \(( 1 \),\( 2 \),\( 3 )\)
The same can be achieved by starting with \( 9 \) and multiplying by \( 1 \), \( 2 \), \( 3 \), \( 4 \), and \( 5 \), giving the pandigital, \( 918273645 \), which is the concatenated product of \( 9 \) and \(( 1 \),\( 2 \),\( 3 \),\( 4 \),\( 5 )\).
What is the largest \( 1 \) to \( 9 \) pandigital \( 9 \)-digit number that can be formed as the concatenated product of an integer with \(( 1 \),\( 2 \), \( ... \) , \( n )\) where \( n>1 \)?