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Guest Message by DevFuse

Ten digits => remarkable number

Best Answer phil1882, 04 August 2014 - 04:43 PM

Spoiler for i cheated and wrote a program to solve
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10 replies to this topic

#1 bonanova

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Posted 03 August 2014 - 11:15 AM

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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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
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#2 wolfgang

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Posted 03 August 2014 - 06:58 PM

Spoiler for The number is

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#3 bonanova

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Posted 03 August 2014 - 08:47 PM

Spoiler for The number is

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

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#4 phil1882

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Posted 04 August 2014 - 04:43 PM   Best Answer

Spoiler for i cheated and wrote a program to solve

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#5 wolfgang

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Posted 04 August 2014 - 08:35 PM

Spoiler for The number is

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

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

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#6 bonanova

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Posted 05 August 2014 - 10:52 AM

Spoiler for I get

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#7 wolfgang

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Posted 05 August 2014 - 04:56 PM

Spoiler for I get

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

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#8 bonanova

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Posted 05 August 2014 - 08:01 PM

Spoiler for I get

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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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#9 Perhaps check it again

Perhaps check it again

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Posted 05 August 2014 - 09:46 PM

Spoiler for I get

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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#10 aristo

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Posted 07 August 2014 - 02:31 PM

the answer to the ten digit remarkable number is

9432581670

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