Originally posted by bobbob1056thWhy shouldn't I give the solution. Other people can solve the puzzle too, if they want without reading the solution. You don't have to read to the solution.
If the puzzle was so GREAT and fun to solve, why did you give the solution?
Originally posted by THUDandBLUNDERAlthough I would much rather you prove its possibility, I will simply state why it makes no sense: There is no way to determine Carols' age. Otherwise the problem is easy:
Get a life. Then a sense of humour. Then justify your bald claim that there is not enough information to determine their ages.
A-30
B-51
C-55
D-46
E-37
(* years of age)
Originally posted by bobbob1056thSo why have you given Carol's age as 55?
Although I would much rather you prove its possibility, I will simply state why it makes no sense: There is no way to determine Carols' age. Otherwise the problem is easy:
A-30
B-51
C-55
D-46
E-37
(* years of age)
And if the problem is easy, show your simple reasoning.
Bernie's age is 70% greater than Ava's, because if it were not, there would not be enough information to solve. From here the rest is simple. One can construct a table of possible ages and see what ages are possible. For example, start off with Ava being 10 years old and go up until there are no contradictions. I suppose you meant to type in Carla instead of Carol.
Originally posted by bobbob1056thWhat a vague handwaving argument! And the rest is simple, eh?
Bernie's age is 70% greater than Ava's, because if it were not, there would not be enough information to solve. .
Originally posted by bobbob1056th
For example, start off with Ava being 10 years old and go up until there are no contradictions.
Construct a table of all possible values and slowly wade through it? How ingenious!
Originally posted by THUDandBLUNDERNo, just start from Ava = 10 and go up until it makes sense.
What a vague handwaving argument! And the rest is simple, eh?
Originally posted by bobbob1056th
[b] For example, start off with Ava being 10 years old and go up until there are no contradictions.
Construct a table of all possible values and slowly wade through it? How ingenious![/b]
Originally posted by PalynkaWell I was just expecting that I'd get a reply in the language that I use (I use north american english). But going back to your original statement, maybe it's that you have the sense of humour; I'm glad I stimulated someones' humour sense! (obviously I don't speak Portugese, either 😉)
So? Why should I use American English?
Debra said to Bernie: "I am 9 years older than Ella."
Ella said to Bernie: "I am 7 years older than Ava."
Ava said to Bernie: "Your age is precisely 70% greater than mine."
Bernie said to Carla: "Ella is younger than you"
Carla said to Debra: "The difference between our ages is 6 years."
Carla said to Ava: "I am 10 years older than you."
Carol said to Ava: "Bernie is younger than Debra."
Bernie said to Carla: "The difference between your age and Debra's age is the same as the difference between Debra's age and Ella's age."
Given that all of the above ladies spoke truthfully when talking to an older woman and lied when talking to a younger woman, what are their actual ages?
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When Carla tells Ava "I'm older than you," she can't be telling the truth.
So it must be a lie, and therefore Carla is older than Ava.
Then Carla's other statement to Ava, "Bernie is younger than Debra", is also a lie.
So Bernie is older than Debra.
If we let > mean 'older than', we have:
C > A
B > D
This means Debra's first statement, "I'm 9 years older than Ella", is true.
So Debra is older than Ella.
By transitivity, Bernie is also older than Ella.
So Ella's statement, "I'm 7 years older than Ava", is true.
So we have:
C > A
B > D > E > A
Suppose Carla is younger than Bernie.
Then Bernie's statement, "Ella is younger than you", would be false.
So Ella would be older than Carla.
We would get:
B > D > E > C > A
But this ordering implies the statement (D to B) "I'm 9 years older than Ella" 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; so we have a contradiction.
Therefore Carla is older than Bernie and we get the ordering:
C > B > D > E > A
We know Debra is 9 years older than Ella from the first statement.
Therefore from the last statement we know Carla must be 9 years older than Debra.
And from the second statment Ella is 7 years older than Ava. This implies that:
C -- 9 years > D -- 9 Years > E -- 7 Years > A
Bernie must be somewhere between Carla and Debra's' ages.
So she is between 17 and 24 years older than Ava.
But, since Bernie's age is exactly 70% greater than Ava's, Ava's age must be divisible by 10.
The only number such that 70% falls between 17 and 24 is 30.
So Ava is 30.
And we have
Ava: 30
Ella: 37
Debra: 46
Bernie: 51
Carla: 55