Hard fraction (Help me)
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From: Dan Cass on 28 Jan 2010 22:19 > Hello Everone > > I try to solve this problem 2 days. > > But can't solve. :P > > Please help me if you can solve.! > > In the picture a, b, c, d, e, f, g, h, i, j are > different digit (0-9) > > http://img25.imageshack.us/img25/1208/hardfractionprob > lem.png > > ab mean a number have 2 digit = 10a + b > > find a, b, c, d, e, f, g, h, i, j at least 5 > solutions. > > TIA Here's one involving a fraction and its repeating decimal. I saw it many years ago, and as I recall it has only one answer. Each capital letter is to be a digit, and the repeating part on the right continues "forever". EVE / DID = .TALKTALKTALK... I liked the humor... Eve did something, and people have been talk,talk,talking about it ever since.
From: Robert Israel on 29 Jan 2010 15:26 Dan Cass <dcass(a)sjfc.edu> writes: > > Hello Everone > > > > I try to solve this problem 2 days. > > > > But can't solve. :P > > > > Please help me if you can solve.! > > > > In the picture a, b, c, d, e, f, g, h, i, j are > > different digit (0-9) > > > > http://img25.imageshack.us/img25/1208/hardfractionprob > > lem.png > > > > ab mean a number have 2 digit = 10a + b > > > > find a, b, c, d, e, f, g, h, i, j at least 5 > > solutions. > > > > TIA > > Here's one involving a fraction and its repeating decimal. > > I saw it many years ago, and as I recall it has only one answer. > > Each capital letter is to be a digit, > and the repeating part on the right continues "forever". > > EVE / DID = .TALKTALKTALK... It's not unique unless you assume that the fraction is in "lowest terms". > I liked the humor... Eve did something, and > people have been talk,talk,talking about it ever since. -- Robert Israel israel(a)math.MyUniversitysInitials.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada
From: Michael Press on 30 Jan 2010 16:11 In article <1509184065.75172.1264771200814.JavaMail.root(a)gallium.mathforum.org>, Dan Cass <dcass(a)sjfc.edu> wrote: > > Hello Everone > > > > I try to solve this problem 2 days. > > > > But can't solve. :P > > > > Please help me if you can solve.! > > > > In the picture a, b, c, d, e, f, g, h, i, j are > > different digit (0-9) > > > > http://img25.imageshack.us/img25/1208/hardfractionprob > > lem.png > > > > ab mean a number have 2 digit = 10a + b > > > > find a, b, c, d, e, f, g, h, i, j at least 5 > > solutions. > > > > TIA > > Here's one involving a fraction and its repeating decimal. > > I saw it many years ago, and as I recall it has only one answer. > > Each capital letter is to be a digit, > and the repeating part on the right continues "forever". > > EVE / DID = .TALKTALKTALK... > > I liked the humor... Eve did something, and > people have been talk,talk,talking about it ever since. Here is the case gcd(EVE, DID) = 1. First 0.000100010001... = 1/9999 = 1/(99 * 101). EVE 1 1 --- = TALK * ---- * --- DID 101 99 Then DID | 101 * 99. DID > 100 so DID = 101 or 303 or 909. EVE < DID so DID != 101. We cannot have DID = 909, for then 11 * EVE = TALK and we would have K = E. If DID = 303 then 33 * EVE = TALK. E != 1 otherwise K = 3. Now E = 2. Since EVE is a multiple of 11 it must be the case that E - V + E is a multiple of 11, hence V = 4. 242 --- = 0.798679867986798679867986... 303 -- Michael Press
From: donno on 31 Jan 2010 13:06
On 31-Jan-2010, Michael Press <rubrum(a)pacbell.net> wrote: > Path: > border1.nntp.dca.giganews.com!nntp.giganews.com!npeer02.iad.highwinds-media.com!news.highwinds-media.com!feed-me.highwinds-media.com!newsfeed1.swip.net!feeder.erje.net!news2.arglkargh.de!news.albasani.net!rubrum > From: Michael Press <rubrum(a)pacbell.net> > Newsgroups: sci.math > Subject: Re: Hard fraction (Help me) > Date: Sat, 30 Jan 2010 13:11:49 -0800 > Organization: Possum Lodge > Lines: 66 > Message-ID: <rubrum-EAB078.13114930012010(a)news.albasani.net> > References: <TsudnbkU56xICfzWnZ2dnVY3go-dnZ2d(a)giganews.com> > <1509184065.75172.1264771200814.JavaMail.root(a)gallium.mathforum.org> > Mime-Version: 1.0 > Content-Type: text/plain; charset=UTF-8 > Content-Transfer-Encoding: 7bit > X-Trace: news.albasani.net > oXXD+AkS8sjruOEJaV7joxLnRxskWidowsr1YaXbuzZ5ZFPUmk7IkwsTyPTHKvWxX6ivX0u3wdjhDOhUwT6fEHWYryGxl6YgRJa+Wc0FZIYm8DuOgcUzrw27g39x1dlN > X-Complaints-To: abuse(a)albasani.net > NNTP-Posting-Date: Sat, 30 Jan 2010 21:11:52 +0000 (UTC) > X-User-ID: uWdZk3K4q+sCGJmMjSCDSEjExb0NAEpC3ZAykZJFCUM= > Cancel-Lock: sha1:10KhlLHHbFyy3QRn/O7sKhfGZr8= > User-Agent: MT-NewsWatcher/3.5.2 (Intel Mac OS X) > X-NNTP-Posting-Host: bvGbXW9JieGssOrU0+1ypyPGrhrMMES/oKTwZHxWpMg= > Bytes: 2737 > Xref: number.nntp.dca.giganews.com sci.math:1274387 > > In article > <1509184065.75172.1264771200814.JavaMail.root(a)gallium.mathforum.org>, > Dan Cass <dcass(a)sjfc.edu> wrote: > > > > Hello Everone > > > > > > I try to solve this problem 2 days. > > > > > > But can't solve. :P > > > > > > Please help me if you can solve.! > > > > > > In the picture a, b, c, d, e, f, g, h, i, j are > > > different digit (0-9) > > > > > > http://img25.imageshack.us/img25/1208/hardfractionprob > > > lem.png > > > > > > ab mean a number have 2 digit = 10a + b > > > > > > find a, b, c, d, e, f, g, h, i, j at least 5 > > > solutions. > > > > > > TIA > > > > Here's one involving a fraction and its repeating decimal. > > > > I saw it many years ago, and as I recall it has only one answer. > > > > Each capital letter is to be a digit, > > and the repeating part on the right continues "forever". > > > > EVE / DID = .TALKTALKTALK... > > > > I liked the humor... Eve did something, and > > people have been talk,talk,talking about it ever since. > > Here is the case gcd(EVE, DID) = 1. > > First > > 0.000100010001... = 1/9999 = 1/(99 * 101). > > EVE 1 1 > --- = TALK * ---- * --- > DID 101 99 > > Then DID | 101 * 99. > DID > 100 so DID = 101 or 303 or 909. > > EVE < DID so DID != 101. > We cannot have DID = 909, > for then 11 * EVE = TALK > and we would have K = E. > > If DID = 303 then 33 * EVE = TALK. > E != 1 otherwise K = 3. > Now E = 2. Since EVE is a multiple of 11 it must be the > case that E - V + E is a multiple of 11, hence V = 4. > > 242 > --- = 0.798679867986798679867986... > 303 > > -- > Michael Press Nice Problem !! :) |