0%

Problem 43


Problem 43


Sub-string divisibility

The number, 1406357289, is a 0 to 9 pandigital number because it is made up of each of the digits 0 to 9 in some order, but it also has a rather interesting sub-string divisibility property.

Let d1 be the 1st digit, d2 be the 2nd digit, and so on. In this way, we note the following:

  • d2d3d4=406 is divisible by 2
  • d3d4d5=063 is divisible by 3
  • d4d5d6=635 is divisible by 5
  • d5d6d7=357 is divisible by 7
  • d6d7d8=572 is divisible by 11
  • d7d8d9=728 is divisible by 13
  • d8d9d10=289 is divisible by 17

Find the sum of all 0 to 9 pandigital numbers with this property.


子串的可整除性

1406357289是一个0至9全数字数,因为它由0到9这十个数字排列而成;但除此之外,它还有一个有趣的性质:子串的可整除性。

记d1是它的第一个数字,d2是第二个数字,依此类推,我们注意到:

  • d2d3d4=406能被2整除
  • d3d4d5=063能被3整除
  • d4d5d6=635能被5整除
  • d5d6d7=357能被7整除
  • d6d7d8=572能被11整除
  • d7d8d9=728能被13整除
  • d8d9d10=289能被17整除

找出所有满足同样性质的0至9全数字数,并求它们的和。