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Topic: Even More Lies (Read 551 times) |
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ThudnBlunder
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Even More Lies
« on: Feb 23rd, 2004, 9:09am » |
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Doris said to Brenda: "I'm 9 years older than Eva."
Eva said to Brenda: "I'm 7 years older than Anne."
Anne said to Brenda: "Your age is exactly 70% greater than mine."
Brenda said to Carol: "Eva is younger than you"
Carol said to Doris: "The difference between our ages is 6 years."
Carol said to Anne: "I'm 10 years older than you."
Carol said to Anne: "Brenda is younger than Doris."
Brenda said to Carol: "The difference between your age and Doris' age is the same as the difference between Doris' age and Eva's age."
If all of the above women spoke the truth when talking to somebody older and lied when speaking to somebody younger, what are their actual ages?
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| « Last Edit: Feb 23rd, 2004, 9:35am by ThudnBlunder » |
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THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you.
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Sameer
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Re: Even More Lies
« Reply #1 on: Feb 23rd, 2004, 1:42pm » |
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We all know women don't age beyond 18 ... or was it 16? 
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"Obvious" is the most dangerous word in mathematics.
--Bell, Eric Temple
Proof is an idol before which the mathematician tortures himself.
Sir Arthur Eddington, quoted in Bridges to Infinity
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Speaker
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Re: Even More Lies
« Reply #2 on: Feb 29th, 2004, 9:57pm » |
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Here is my answer:
Carol = 62
Brenda = 51
Doris = 46
Eva = 37
Anne = 30
I started with the premise that Carol could not truthfully say that she was older than another person. Which gave me Carol being older and lying to Anne. Then I figured that to be exactly 70% older limited the ages to 10/17, 20/34, 30/51. So, I tried them and got the age of Brenda and Anne, then addition and subtraction to get Doris and Eva.
Carol gave me a little trouble, but I just tried her telling the truth or lying, and worked it out. Of course I made some charts that were alternately confusing and helpful.
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ThudnBlunder
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Re: Even More Lies
« Reply #3 on: Mar 1st, 2004, 10:29am » |
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Speaker, your answer does not square with the last statement.
(It is possible to arrive at a solution without any guesswork.) 
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Sameer
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Re: Even More Lies
« Reply #4 on: Mar 1st, 2004, 10:52am » |
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I could only produce this chart: Maybe that will be helpful to people.. I cannot solve it at the moment
-------------
|-----------|
v-----------^
D --> B --> C --> A
^-----------v
/ |-----------|
E -----------
It basically meanst D&B should imply C
B&C should imply A
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| « Last Edit: Mar 1st, 2004, 10:56am by Sameer » |
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"Obvious" is the most dangerous word in mathematics.
--Bell, Eric Temple
Proof is an idol before which the mathematician tortures himself.
Sir Arthur Eddington, quoted in Bridges to Infinity
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Speaker
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Re: Even More Lies
« Reply #5 on: Mar 1st, 2004, 6:51pm » |
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Okay, I made a mistake, so sue me.
Here is the corrected and I hope correct answer. I only had one wrong last time, I missed Carol's age by 7 years.
Anne 30
Brenda 51
Carol 55
Doris 46
Eva 37
In alphabetical order this time. 
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They that can give up essential liberty to obtain a little temporary safety deserve neither liberty nor safety. <Ben Franklin>
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Icarus
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Re: Even More Lies
« Reply #6 on: Mar 2nd, 2004, 3:32pm » |
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on Mar 1st, 2004, 6:51pm, Speaker wrote:| Okay, I made a mistake, so sue me. |
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Carol's lawyer will be contacting you shortly about her libel suit.  She was most incensed at the insult!
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ThudnBlunder
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Re: Even More Lies
« Reply #7 on: Mar 23rd, 2004, 8:22am » |
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:When Carol tells Anne "I'm older than you," she can't be telling the truth.
So it must be a lie, and therefore Carol is older than Anne.
Then Carol's other statement to Anne, "Brenda is younger than Doris", is also a lie.
So Brenda is older than Doris.
If we let > mean 'older than', we have:
C > A
B > D
This means Doris's first statement, "I'm 9 years older than Eva", is true.
So Doris is older than Eva.
By transitivity, Brenda is also older than Eva.
So Eva's statement, "I'm 7 years older than Anne", is true.
So we have:
C > A
B > D > E > A
Suppose Carol is younger than Brenda.
Then Brenda's statement, "Eva is younger than you", would be false.
So Eva would be older than Carol.
We would get:
B > D > E > C > A
But this ordering implies the statement (D to B) "I'm 9 years older than Eva" is true.
And that the statment (C to D) "The difference between our ages is 6 years" is also true.
But clearly both cannot be true, a contradiction.
Therefore Carol is older than Brenda and we get the ordering:
C > B > D > E > A
We know Doris is 9 years older than Eva from the first statement.
Therefore from the last statement we know Carol must be nine years older than Doris.
And from the second statment Eva is 7 years older than Anne. This implies that:
C -- 9 years > D -- 9 Years > E -- 7 Years > A
Brenda must be somewhere between Carol and Doris' ages.
So she is between 17 and 24 years older than Anne.
But, since Brenda's age is exactly 70% greater than Anne's, Anne's age must be divisible by 10.
The only number such that 70% falls between 17 and 24 is 30.
So Anne is 30.
And we have
Anne: 30
Eva: 37
Doris: 46
Brenda: 51
Carol: 55
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