Thread: Finding how many 8 digit numbers, with a twist

I need to find how many 8 digit numbers exists that have no zeros in them and each of the other digits (1-9) may only occur once. (no repeats)

Also the numbers must be devisable with three.

Please help, i have been trying to figur this one out for a while but i am really stuck.

Regards Monika

Originally Posted by Monika1987

I need to find how many 8 digit numbers exists that have no zeros in them and each of the other digits (1-9) may only occur once. (no repeats) Also the numbers must be divisible with three.

Any number divisible three must have the sum of its digits divisible by three.
Note that thus if we add any two of we have an eight-digit number divisible by three.
Note also that those are the only eight-digit numbers divisible by three.
Rearrange each set. What is the total?