bonanova Posted August 3, 2014 Report Share Posted August 3, 2014 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 digit (4) is divisible by 1 - OK two digits (46) is divisible by 2 - OK three digits (462) is divisible by 3 - so far, so good ... four digits (4623) is divisible by 4 - Oops ...guess not. five digits is divisible by 5 six digits is divisible by 6 seven digits is divisible by 7 eight digits is divisible by 8 nine digits is divisible by 9 ten digits (the entire number) is divisible by 10 - Aha! The last digit is zero. And digit 5 must be ... Quote Link to comment Share on other sites More sharing options...

0 phil1882 Posted August 4, 2014 Report Share Posted August 4, 2014 3816547290 Quote Link to comment Share on other sites More sharing options...

0 wolfgang Posted August 3, 2014 Report Share Posted August 3, 2014 9632581470 the 5th digit must be 5 Quote Link to comment Share on other sites More sharing options...

0 bonanova Posted August 3, 2014 Author Report Share Posted August 3, 2014 9632581470 the 5th digit must be 5 Very close, wolfgang, but check out the first eight digits. Quote Link to comment Share on other sites More sharing options...

0 wolfgang Posted August 4, 2014 Report Share Posted August 4, 2014 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... Quote Link to comment Share on other sites More sharing options...

0 bonanova Posted August 5, 2014 Author Report Share Posted August 5, 2014 963258147 / 8 = 120407268.375 Quote Link to comment Share on other sites More sharing options...

0 wolfgang Posted August 5, 2014 Report Share Posted August 5, 2014 963258147 / 8 = 120407268.375 but these are 9 digits and not 8 , so you should devide the number by 9. Quote Link to comment Share on other sites More sharing options...

0 bonanova Posted August 5, 2014 Author Report Share Posted August 5, 2014 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 Quote Link to comment Share on other sites More sharing options...

0 Perhaps check it again Posted August 5, 2014 Report Share Posted August 5, 2014 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. Quote Link to comment Share on other sites More sharing options...

0 aristo Posted August 7, 2014 Report Share Posted August 7, 2014 the answer to the ten digit remarkable number is 9432581670 Quote Link to comment Share on other sites More sharing options...

0 Perhaps check it again Posted August 8, 2014 Report Share Posted August 8, 2014 aristo, your candidate for an answer fails, for instance, when seeing that 943 is not divisible by 3. Quote Link to comment Share on other sites More sharing options...

## Question

## bonanova

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

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