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You are not logged in. #1 20121203 00:55:19
Double and halfFind a natural number for which, if you move its first digit at the end, you get a number that is half the original one Last edited by anna_gg (20121203 02:16:06) #2 20121203 02:16:57
Re: Double and halfHi anna_gg; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #3 20121203 02:19:55
Re: Double and half
Bobbym, #4 20121203 02:46:58
Re: Double and halfHi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #5 20121203 04:34:34
Re: Double and half
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 15,000,000. Then I gave up #6 20121203 11:28:42
Re: Double and halfHi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #7 20121203 15:51:02
Re: Double and halfSuppose 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 18digit number. PS: Yes, there are infinitely many solutions, because there are infinitely many n such that is divisible by 19. Last edited by scientia (20121203 15:54:02) #8 20130227 00:08:24
Re: Double and halfHere 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 20130227 11:25:03
#10 20130301 03:39:16
Re: Double and half
CORRECT! I found it by using Excel but now am trying to formulate it. #11 20130302 02:06:52
Re: Double and halfHi anna_gg, 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 END Last edited by phrontister (20130304 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 20130317 10:54:06
Re: Double and halfSo, we generalize the problem as follows: 134 books currently added on Goodreads 