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# Ten digits => remarkable number

## Question

This time there are all ten digits: 0 1 2 3 4 5 6 7 8 9

I just made a single number, using each of them exactly once: like 4623901875.

Can you guess my number?

Of course you need some clues: (and we'll see whether 4623901875 fits.)
The number formed by the first

1. digit (4) is divisible by 1 - OK
2. two digits (46) is divisible by 2 - OK
3. three digits (462) is divisible by 3 - so far, so good ...
4. four digits (4623) is divisible by 4 - Oops ...guess not.
5. five digits is divisible by 5
6. six digits is divisible by 6
7. seven digits is divisible by 7
8. eight digits is divisible by 8
9. nine digits is divisible by 9
10. ten digits (the entire number) is divisible by 10 - Aha! The last digit is zero. And digit 5 must be ...

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3816547290

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9632581470

the 5th digit must be 5
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9632581470

the 5th digit must be 5

Very close, wolfgang, but check out the first eight digits.

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9632581470

the 5th digit must be 5

Very close, wolfgang, but check out the first eight digits.

I did...and I didn`t find any mistake...

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963258147 / 8 = 120407268.375
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963258147 / 8 = 120407268.375

but these are 9 digits and not 8 , so you should devide the number by 9.

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963258147 / 8 = 120407268.375

but these are 9 digits and not 8 , so you should devide the number by 9.

You're right of course.  I meant to point out that 96325814 / 8 = 12040726.75

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963258147 / 8 = 120407268.375

but these are 9 digits and not 8 , so you should devide the number by 9.

You're right of course.  I meant to point out that 96325814 / 8 = 12040726.75

It is sufficient to check that 814 divided by 8 does not equal an integer

to know that 96325814 divided by 8 will not give an integer.

Suppose that an integer is at least four digits long.

That integer is divisible by 8 if the number formed by the three

rightmost digits is divisible by 8.  If the number formed by the

three rightmost digits is not divisible by 8, then the original

number is not divisible by 8.

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the answer to the ten digit remarkable number is

9432581670

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aristo, your candidate for an answer fails, for instance, when seeing that

943 is not divisible by 3.

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