# Thread: Need help with American Billion problem

1. ## Need help with American Billion problem

I need help finding a number, please post only clues and not an answer.

'Find a ten-digit number which uses each of the digits 0-9 once and has the following properties'
First digit is divisible by 1
Number formed by the first 2 digits from the left is divisible by 2
Number formed by the first 3 digits from the left is divisible by 3
(so on...up to 9)
Number itself is divisible by 10

I've worked out that there are 9 different possibilities for the first 3 numbers, I think 15 for the first 4 (please tell me if I'm wrong, but only give a clue not the answer) and 16 for the first 5.

I just have no idea how to incorporate the idea that although a number is a possibility for example statement 3 or 4, it may not be possible for the 7th statement (Number formed by the first 7 digits...). Nor how I can check these possibilities and see if all their numbers are different.

No calculator, (yes a spreadsheet would be great, but no ), and no A-level maths or higher.

I need to find a number but preferrably how many numbers that correspond to these rules exist.

Thanks.

2. Originally Posted by Mukilab
I need help finding a number, please post only clues and not an answer.

'Find a ten-digit number which uses each of the digits 0-9 once and has the following properties'
First digit is divisible by 1
This no restriction at all, every digit is "divisible by 1"

Number formed by the first 2 digits from the left is divisible by 2
This tells you that the second digit is divisible by 2: 2, 4, 6, 8, or 0 but still no conditon on the first digit.

[quote]Number formed by the first 3 digits from the left is divisible by 3[quote]
This tells you that the sum of the first three digits is divisible by 3.

(so on...up to 9)
I take that this means the number made by the first 4 digits is divisible by 4, the fist 5, divisible by 5, the first 6 is divisible by 6, etc.
The fact the number made by the first 4 digits is dividibler by 4 means that the number made by the third and fouth digits is divisible by 4. The fact that the number made by the first 5 digits is divisible by 5 tells you that the 5th digit is either 5 or 0.

Number itself is divisible by 10
which means simply that the last digit is 0.

I've worked out that there are 9 different possibilities for the first 3 numbers, I think 15 for the first 4 (please tell me if I'm wrong, but only give a clue not the answer) and 16 for the first 5.

I just have no idea how to incorporate the idea that although a number is a possibility for example statement 3 or 4, it may not be possible for the 7th statement (Number formed by the first 7 digits...). Nor how I can check these possibilities and see if all their numbers are different.

No calculator, (yes a spreadsheet would be great, but no ), and no A-level maths or higher.

I need to find a number but preferrably how many numbers that correspond to these rules exist.