How do I solve this math problem? The digits 1, 2, 3, 4, 5, 6, 7, 8, and 9 are each used once in some order to compose a single 9-digit number. Starting from the leftmost digit, the first digit is divisible by 1, the first two are divisible by 2, the first three digits are divisible by 3, and so on ending with 9-digit number being divisible by 9. What is the number?? PLEASE SHOW ALL YOUR WORK!!! 

Expert Answers

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381,654,729

While it would be impossible for me to show all of the work here, there are some basic rules that can help. 

The first digit can be anything since all whole numbers can be divided by 1.  For 2, make sure it ends in an even number.  For the third position, just add up all three of the digits, if the sum is divisible by 3 then you are ok.  For 4, check the last two numbers.  If they are divisible by 4, it works. The 5th position has to be a 5 in order for it to be divisible by 5. So, the number will be: odd-even-odd-even-5-even-odd-even-odd. For 6, make sure it is divisible by 3 (see above) and it ends in an even number. No good tricks for 7 I am afraid, but you only have 2 odd numbers left, so it won't be hard to figure it out.  On eights, just follow the rule for 4. All combinations will be divisible by nine, so don't worry here.

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