make up a 9 digit number so that...?

Question

use each number exactly once
*the first 2 digits comprise a 2 digit # divisible by 2
*first 3 comprise a 3 digit # divisible by 3....
and so on...
*the first 8 digits comprise and 8 digit # divisible by 8..
*the entire number is divisible by 9

Answer 1

381654729


38 / 2 = 19
381 / 3 = 127
3816 / 4 = 954
38165 / 5 = 7633
381654 / 6 = 63609
3816547 / 7 = 545221
38165472 / 8 = 4770684
381654729 / 9 = 42406081

Answer 2

Here's how to find it:

- Starting with all 9 digits unknown...
xxxxxxxxx

- The 5th digit must be a 5...
xxxx5xxxx

- 2nd, 4th, 6th and 8th digits must be even (others are odd) so the first 2 digits, first 4 digits etc make an even number.
- 3rd digit is odd so the 4th digit must be 2 or 6 to get a multiple of 4.
xxx25xxxx or xxx65xxxx

- sum of first 3 digits is divisible by 3, so the sum of the next 3 digits must also be divible by 3 (so the first 6 digits are a multiple of 6). The only possibilities for an even 6th digit are...
xxx258xxx or xxx654xxx

- Fill in the remaining even numbers:
x4x258x6x or
x6x258x4x or
x8x654x2x or
x2x654x8x

- Need a multiple of 8 in digits 6, 7 and 8, the only possibilities are:
x4x25816x or
x4x25896x or
x8x65432x or
x8x65472x

- First 3 digits are a multiple of 3 → so are next 3 digits → so are the last 3 digits. This leaves...
x4x258963 or
x8x654321 or
x8x654327 or
x8x654723 or
x8x654729

- At this point the only condition still up in the air is the one concerning the first 7 digits. Fill in the remaining two digits and see if we get a multiple of 7 in the first 7 digits:

381654729 is the only one that works.

Answer 3

Holy smokes...how did links305 figure that out?