126. Find a Number Consisting of 9 Digits
Find a number consisting of 9 digits in which each of the digits from 1 to 9 appears only once. This number should satisfy the following requirements:
a. The number should be divisible by 9.
b. If the most right digit is removed, the remaining number should be divisible by 8.
c. If then again the most right digit is removed, the remaining number should be divisible by 7.
d. etc. until the last remaining number of one digit which should be divisible by 1.
Submitted by tartle · Added 17 January 2013
Solution:
The number that satisfies all the conditions is 381654729. It is a 9-digit number using each digit from 1 to 9 exactly once, is divisible by 9, and removing digits from the right results in numbers that are divisible by 8, 7, 6, 5, 4, 3, 2, and 1 respectively.
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381654729
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