Mysterious Number: Find the Solution June 5

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I'm a natural number written with 10 different digits such that for all i ∈ {1,...,10} the number formed by my i first digits (from left to right) is divisible by i. Who am I?

- All solutions will be posted June 5.

 

[jvicens]

After analyzing the given criteria, it can be concluded that the number in question is 3816547290. This number satisfies all the given conditions as follows:

- The first digit, 3, is divisible by 1.
- The first two digits, 38, are divisible by 2.
- The first three digits, 381, are divisible by 3.
- The first four digits, 3816, are divisible by 4.
- The first five digits, 38165, are divisible by 5.
- The first six digits, 381654, are divisible by 6.
- The first seven digits, 3816547, are divisible by 7.
- The first eight digits, 38165472, are divisible by 8.
- The first nine digits, 381654729, are divisible by 9.
- The first ten digits, 3816547290, are divisible by 10.

Therefore, the number in question is 3816547290.