Divisive

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Find a 10 digit number that has all the digits from 0 to 9 in it. The number is such that the first digit is divisible by 1. First 2 digits divisible by 2, first 3 by 3, first 4 by 4, so on and finally the ten digit number is divisible by 10.

Alan

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7296541830

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Very close, but 72965418

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Got there, at last, by using the rules of divisibilty.

3816547290

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Nice one Rob. I also had to rattle my brain on those old rules of divisibility. Even then, it didn’t jump out and bite me – just reduced the amount of trial & error.

Alan

Edited – Extension –
Divisibility checks for 2,3,4,5,6,8,9 or 10 are fairly well known and easily derived.
But how do you check for divisibility by 7?

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(Edited by tony55 on 06-Sep-04 18:18. )

I once knew the divisibility rules up to 13, just been thinking about them and those for 11 and 13 are escaping me at the moment (probably be able to find them easy enough by googling). As for divisibility by 7:

You take the last digit of the number and double it. Subtract this from the rest of the number. If the answer is divisible by 7 including cases where the answer is 0, then the number is divisible by 7

Added: Just googled and now I remember the answer for 11 and 13

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Once at university, I asked some lecturers to prove the 3 and 11 ones.

Some of these others look like they would have good proofs too.

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Once at university, I asked some lecturers to prove the 3 and 11 ones.

Some of these others look like they would have good proofs too.

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Isn’t the pain of applying the ‘divisible by 7’ rule just about the same as actually dividing the original number by 7?

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Tim

I agree, the same also applies for the ‘divisible by 13’ rule. In an age when many people now reach for a calculator when asked to do even the simplest arithmetic it is a moo point

ps do schools teach divisibility rules any more?

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I doubt it! I was asking a year 11 student what you get if you try to divide a number by zero. She answered “error”. It took me a while to twig that she meant:

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I doubt it! I was asking a year 11 student what you get if you try to divide a number by zero. She answered “error”. It took me a while to twig that she meant:

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Tim

I agree, the same also applies for the ‘divisible by 13’ rule. In an age when many people now reach for a calculator when asked to do even the simplest arithmetic it is a moo point

ps do schools teach divisibility rules any more?

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Isn’t the pain of applying the ‘divisible by 7’ rule just about the same as actually dividing the original number by 7?

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(Edited by tony55 on 06-Sep-04 18:18. )

I once knew the divisibility rules up to 13, just been thinking about them and those for 11 and 13 are escaping me at the moment (probably be able to find them easy enough by googling). As for divisibility by 7:

You take the last digit of the number and double it. Subtract this from the rest of the number. If the answer is divisible by 7 including cases where the answer is 0, then the number is divisible by 7

Added: Just googled and now I remember the answer for 11 and 13

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Nice one Rob. I also had to rattle my brain on those old rules of divisibility. Even then, it didn’t jump out and bite me – just reduced the amount of trial & error.

Alan

Edited – Extension –
Divisibility checks for 2,3,4,5,6,8,9 or 10 are fairly well known and easily derived.
But how do you check for divisibility by 7?

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Got there, at last, by using the rules of divisibilty.

3816547290

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Very close, but 72965418

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7296541830

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