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#1 2012-12-03 00:55:19
- anna_gg
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Double and half
Find a natural number for which, if you move its first digit at the end, you get a number that is half the original one
(e.g. 81345--->13458 but the resulting number must be the half of the original).
Last edited by anna_gg (2012-12-03 02:16:06)
#2 2012-12-03 02:16:57
- bobbym
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Re: Double and half
Hi anna_gg;
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#3 2012-12-03 02:19:55
- anna_gg
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Re: Double and half
bobbym wrote:
Hi anna_gg;
Bobbym,
Sorry, I had made a mistake - please read the new description!
#4 2012-12-03 02:46:58
- bobbym
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Re: Double and half
Hi;
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#5 2012-12-03 04:34:34
- anna_gg
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Re: Double and half
bobbym wrote:
Hi;
Great! It is said that there are infinitely many solutions. I have used Excel for the calculations but have not been able to find any at the range 1-5,000,000. Then I gave up 
#6 2012-12-03 11:28:42
- bobbym
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Re: Double and half
Hi;
There are more solutions.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#7 2012-12-03 15:51:02
- scientia
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Re: Double and half
Suppose the number is
NB:
(i) Since the number must be even, I write for the last digit; .
(ii) and cannot be zero but the other can be 0.
So we want
i.e.
As the LHS is divisible by 19, so must the RHS, and as we must have divisible by 19. The smallest such n is – in other words, the smallest solution is an 18-digit number.
PS: Yes, there are infinitely many solutions, because there are infinitely many n such that is divisible by 19.
Last edited by scientia (2012-12-03 15:54:02)
#8 2013-02-27 00:08:24
- anna_gg
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Re: Double and half
Here is another variation: Find the smallest natural number for which, if you move its last digit at the beginning, you get a number that is 5 times the original.
#9 2013-02-27 11:25:03
- scientia
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#10 2013-03-01 03:39:16
- anna_gg
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Re: Double and half
scientia wrote:
CORRECT! I found it by using Excel but now am trying to formulate it.
#11 2013-03-02 02:06:52
- phrontister
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Re: Double and half
Hi anna_gg,
Try the following in Excel (I use v2007):-
And here's a little program in BASIC, but testing more numbers, with the same single result (142857):
Code:
FOR n = 10 TO 5000000000 STEP 5
n$ = STR$(n)
a$ = RIGHT$(n$,LEN(n$)-1) + LEFT$(n$,1)
IF VAL(a$)*5 - n = 0 THEN PRINT a$
NEXT n
ENDLast edited by phrontister (2013-03-04 23:40:44)
"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson
#13 2013-03-17 10:54:06
- Nehushtan
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Re: Double and half
So, we generalize the problem as follows:
Find the smallest natural number of two or more digits such that if you move the last digit to the front, the resulting number will be n times the original number.
Here are my calculations:
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