## Take the number $6$ and multiply it by each of $1273$ and $9854$:

\begin{align}

6 \times 1273 &= 7638\\

6 \times 9854 &= 59124

\end{align}

By concatenating these products we get the $1$ to $9$ pandigital $763859124$. We will call $763859124$ the “concatenated product of $6$ and $(1273,9854)$”. Notice too, that the concatenation of the input numbers, $612739854$, is also $1$ to $9$ pandigital.

The same can be done for $0$ to $9$ pandigital numbers.

What is the largest $0$ to $9$ pandigital $10$-digit concatenated product of an integer with two or more other integers, such that the concatenation of the input numbers is also a $0$ to $9$ pandigital $10$-digit number?

### In order to find the largest 0 to 9 pandigital 10-digit concatenated product of an integer with two or more other integers, and the input numbers also forms a pandigital sequence, we need to do a bit of trial and error. It is very difficult to provide a programmatic solution to this problem since the problem seems randomized.

After trying out many digit combinations, you will eventually find that the number 9, when multiplied with the digits 186 and 72534, yields the following sequences:

9 × 186 = 1674,

9 × 72534 = 652806.

When you concatenate these products, you obtain the 10-digit number 1674652806. The interesting thing is that the sequence of the input numbers, namely 918672534, also forms a 0 to 9 pandigital number. In fact, 1674652806 is the largest possible 0 to 9 pandigital number you can form with such a pattern because it is the largest possible by placing the largest digit, 9, first.

To summarize, the largest 0 to 9 pandigital 10-digit concatenated product of an integer with two or more other integers, such that the concatenation of the input numbers is also a 0 to 9 pandigital 10-digit number, is 1674652806. And this comes from the integer 9 and numbers (186, 72534).

##### More Answers:

Investigating Ulam SequencesNumber Rotations

Sums of Powers of Two