I have a mathematical puzzle for you...?

Question

Consider a ten-digit number with the following properties: each digit from 0-9 occurs in the number exactly once. The number itself is divisible by ten. If you remove the last digit, the nine-digit number so formed is divisible by nine. If you remove the last two digits, the eight-digit number so formed is divisible by eight. If you remove the last three digits, the seven digit number so formed is divisible by seven, and in general the n-digit number formed from the first n digits is divisible by n. Call any number with all of these properties Pascalian. Now the question:

Part A: List all the Pascalian numbers, if any exist.
Part B: Show, by human-verifiable proof, that such a list is exhaustive.

You may wish to make use of the following information in solving this problem: http://en.wikipedia.org/wiki/Divisibility_rule

Good luck.

That's good superobotz, but can you prove that it's the only one?

Answer 1

There is a rather long proof of this puzzle at the link below.

Answer 2

Part A:

There's only one: 3816547290.

Part B:

There are only a certain amount of possibilities of ten digit numbers, so the list must be exhaustive.

Answer 3

this is the easiest question anyone has ever asked me ever
start with five ones--- 11111
add 6 to any 3 of these
rewrite the prime number to the extent that the number is a repitition like 1711717117
the proof is easy
there is an exhaustive range of permutations for prime numbers repeating themselves
prime numbers do these kinds of properties because when you graph them, and then regraph them on top of each other, you get that number's equation in nth dimensional geometric gravitational symmetry of magnetic encirclement, its like a song if you will, composed mostly of morse code, that repeats itself on top of itself, like a heartbeat, so perhaps your proof is that i can move things in telekinetic fashion using a human hand as my basis for magnetic harmony being played with. beyond these permutative proofs i cannot but begin to remind you that all prime numbers rewrite themselves if givin the proper frame of mind, autistics are so very very good at this. Thanks for the refresher i love answering silly little things like this.