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Thread: Divisive

20040903, 13:56 #1
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Divisive
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

20040903, 15:35 #2
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Re: Divisive
<span style="backgroundcolor: #FFFF00; color: #FFFF00; fontweight: bold">7296541830</span hide>
<font color=blue><font face="Script MT Bold"><big>Rob</big></font face=script></font color=blue>

20040904, 00:03 #3
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Re: Divisive
Very close, but <span style="backgroundcolor: #FFFF00; color: #FFFF00; fontweight: bold">72965418

20040904, 11:52 #4
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Re: Divisive
Got there, at last, by using the rules of divisibilty.
<span style="backgroundcolor: #FFFF00; color: #FFFF00; fontweight: bold">3816547290</span hide><font color=blue><font face="Script MT Bold"><big>Rob</big></font face=script></font color=blue>

20040906, 13:28 #5
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Re: Divisive
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?

20040906, 16:18 #6
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Re: Divisive
<P ID="edit" class=small>(Edited by tony55 on 06Sep04 18:18. )</P>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:
<span style="backgroundcolor: #FFFF00; color: #FFFF00; fontweight: bold">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</span hide>
Added: Just googled and now I remember the answer for 11 and 13

20040908, 07:18 #7
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Re: Divisive
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.

20040908, 10:57 #8
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Re: Divisive
Isn't the pain of applying the 'divisible by 7' rule just about the same as actually dividing the original number by 7?
(Location Australia, then UK, but now USA. Heart, outlook, attitude, etc always Australian)
Quote: "All Happiness is the release of internal pressure"

20040908, 11:38 #9
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Re: Divisive
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?

20040908, 13:26 #10
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Re: Divisive
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: