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How it Started (Eve Did Talk) (Posted on 2003-12-10) Difficulty: 3 of 5
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?

See The Solution Submitted by DJ    
Rating: 4.1429 (7 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Solution (no computer program used) | Comment 1 of 7
.TALKTALKTALK... is TALK/9999, and 9999 = 3x3x11x101, so good candidates for DID are 101, 303 and 909, and then TALK would be EVE*99 (not likely--I'd say impossible, actually), EVE*33, or EVE*11. But if EVE*11 were TALK then E would be K, and that's no good.

So EVE*33 should come out to TALK, while DID is 303. E can't be a 1 as then K would be 3, but D is already 3. If E were 4 the product times 33 would come out too high, and 3 is already taken, so E is 2.

212*33=6996 which isn't TALK. The next available digit for V is 4, and 242*33=7986, which can indeed be TALK.

So we get 242/303=.79867986...
  Posted by Charlie on 2003-12-10 09:56:19
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