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Problem 38


Problem 38


Pandigital multiples

Take the number 192 and multiply it by each of 1, 2, and 3:

192 × 1 = 192
192 × 2 = 384
192 × 3 = 576

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?


全数字的倍数

将192分别与1、2、3相乘:

192 × 1 = 192
192 × 2 = 384
192 × 3 = 576

连接这些乘积,我们得到一个1至9全数字的数192384576。我们称192384576为192和(1,2,3)的连接乘积。

同样地,将9分别与1、2、3、4、5相乘,得到1至9全数字的数918273645,即是9和(1,2,3,4,5)的连接乘积。

对于n > 1,所有某个整数和(1,2, … ,n)的连接乘积所构成的数中,最大的1至9全数字的数是多少?