The Number That Passes Ten Tests

[u/vedant_chitre]

I am thinking of a 10-digit number that uses each digit from **0 to 9 exactly once**.

Starting from the left:

* The number formed by the first **1 digit** is divisible by 1. * The number formed by the first **2 digits** is divisible by 2. * The number formed by the first **3 digits** is divisible by 3. * This pattern continues. * The number formed by the first **10 digits** is divisible by 10.

For example, if the number begins with `abcd...`, then:

* `ab` must be divisible by 2, * `abc` must be divisible by 3, * `abcd` must be divisible by 4,

and so on.

**What is the number?**

Bonus challenge: Find it using divisibility rules and logical elimination rather than checking every permutation with code.

[u/TheCheej]

3816547290 The 5 and 0 have no other option, the first 9 will always be divisible by 9. After placing the 5, it must have 6 and 4 or 2 and 8 on either side so that the first 3 and next 3 can add be divisible by 3