Problem 43 // Project Euler

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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 1^st digit, d₂ be the 2^nd 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 p 大专栏  Problem 43 // Project Eulerandigital numbers with this property.

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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。

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