perplexus.info :: Word Problems : How it Started (Eve Did Talk)

How it Started (Eve Did Talk) (Posted on 2003-12-10)

Ever wonder why women talk so much? It all started with Eve, and not only did she talk, but she kept on talking forever (if only through the generations of women to come).

The following equation, in which each letter represents a different digit, shows this phenomenon as an infinitely repeating decimal:

EVE/DID=.TALKTALKTALKTALK...

What number does each letter represent?

Submitted by DJ

Rating: 4.1429 (7 votes)

Solution: (Hide)

There are a number of ways to show that 0.TALKTALKTALKTALK...=TALK/9999. I will not go into that detail here.

So EVE/DID=TALK/9999. The equation will solve for integer values, certainly, if DID is a factor of 9999. The prime factors of 9999 are 3, 3, 11, and 101. The factors of 9999 of the form DID are 101, 303, and 909. Also we know that E < D.

A great deal of experimenting with the other numbers shows that there is only one solution of this type:

242/303=.798679867986... 0 1 2 3 4 5 6 7 8 9 I - E D V - K T L A
Of course, DID needs not necessarily be a factor of 9999. Rather, it must be a factor of 9999*EVE. Much more experimenting with all of the numbers shows that there is a second solution:

212/606=.3498349834983498... 0 1 2 3 4 5 6 7 8 9 I V E T A - D - K L

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
No Subject	Clinton Faulkner	2022-10-17 10:23:13
No Subject	Clinton Faulkner	2022-10-10 08:40:29
No Subject	Clinton Faulkner	2022-09-28 10:36:58
No Subject	Clinton Faulkner	2022-09-21 10:56:53
No Subject	Clinton Faulkner	2022-09-20 06:47:41
No Subject	Ian Salas	2022-09-13 11:37:59
https://www.swatsonsolutions.com/	Graham Winters	2022-08-25 09:39:55
idriptherapy.com	Graham Winters	2022-08-22 09:56:02
No Subject	Graham Winters	2022-08-16 08:50:22
No Subject	Graham Winters	2022-08-12 09:57:52
highlighter pens	Graham Winters	2022-08-11 12:37:52
No Subject	Tamara Acevedo	2022-07-27 12:33:29
netsuite training	Scarlet Mckinney	2022-07-25 08:43:26
สล็อต 888	Avram Merrill	2022-07-20 08:51:20
Essay	Avram Merrill	2022-07-19 09:13:05
houses for sale	Avram Merrill	2022-06-23 09:11:56
No Subject	McKenzie Ramos	2021-12-10 00:01:21
wigs	Neve Moreno	2021-09-27 23:53:08
re(2): Solution--not unique (computer program used this time)	Buffy Gregory	2021-06-26 04:26:06
solution	K Sengupta	2007-03-05 04:15:50
re(4): Solution--not unique (computer program used this time)	Richard	2003-12-10 18:10:26
re(3): Solution--not unique (computer program used this time)	Charlie	2003-12-10 13:19:44
re(2): Solution--not unique (computer program used this time)	Richard	2003-12-10 13:08:35
re(2): Solution--not unique (computer program used this time)	Charlie	2003-12-10 11:35:46
re: Solution--not unique (computer program used this time)	Charlie	2003-12-10 11:29:39
Solution (no computer program used)	Charlie	2003-12-10 09:56:19

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