arranging digits

[Guest gez]

Can you arrange the digits 1,2,3,4,5,6,7,8,9

in an order so that the number formed by the first number formed by the first 2 digits is divisible by 2. First 3 digits

divisible by 3. First four digits is divisible by 4 and the first 5

digits is divisible by 5 and so on up to nine digits?

 

 

12 is divisible by 2, 123 is divisible by 3, 1236 is divisible by 4,

12365 is divisible by 5, 123654 is divisible by 6 but 1236549 is not divided by 7!

 

i hope you can help thankz!

[JaKiri]

The 1st must be odd, the 2nd even, and so on, to allow the even numbers to divide your result. Similarly, the 5th must be 5, and it doesn't matter what the 9th is, as any combination of those numbers will be divisable by 9.

 

Find a 7 digit number divisable by 7 of this form, and backtrack.

[Guest gez]

thankz you but can you tell me the answer? plez

he he know that definitely helped

[Guest e-Monk]

Okay, I found three such numbers; they are:

381654729

781654329

983654721

 

I believe there aren't any other. You can either reason to get these numbers or you can be a smartass and write a simple code loop in the language of your choice to find them; either way wouldn't take too long.