Problem 170

Find the largest 0 to 9 pandigital that can be formed by concatenating products

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

6 × 1273 = 7638
6 × 9854 = 59124

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?

求用乘积拼接而成的最大0至9全数字数

将6分别乘以1273和9854：

6 × 1273 = 7638
6 × 9854 = 59124

连接这两个乘积我们得到1至9全数字数763859124.我们称763859124为“6和(1273,9854)乘积的连接”。注意到，被乘的这些数的连接612739854，同样也是1至9全数字数。

对于0至9全数字数也存在同样的可能。

在所有由一个整数和另外至少两个整数的乘积连接而成且被乘的整数连接起来也是0至9全数字数的0至9全数字数中，求其中最大的一个。