Ina Meena Dika
Mr. Tito collecting data for census came across a house with three sisters Ina, Meena, and Dika. There were no straight answers when he enquired about their ages. This is what he was told
Ina said "All of us are above 24 years of age, Dika is the youngest, and ofcourse I am the eldest."
"The difference between Dika's age and mine is three years and the sum of my age and Ina's age is two more that twice Dika's age" told mathematician Meena. I am eldest if and only if Dika is not the youngest, she added.
Dika was more "clear" than others , she said "Meena is elder to me" and "Either I am 24 years old or Ina 25 or Meena 26" She added one more piece of vital information "Meena is not 27 years old"
To add to the confusion, Mr. Tito was told by a neighbour that one of the sister always lies and the other two always speak the truth. Can you help him find the ages?
Ina said "All of us are above 24 years of age, Dika is the youngest, and ofcourse I am the eldest."
"The difference between Dika's age and mine is three years and the sum of my age and Ina's age is two more that twice Dika's age" told mathematician Meena. I am eldest if and only if Dika is not the youngest, she added.
Dika was more "clear" than others , she said "Meena is elder to me" and "Either I am 24 years old or Ina 25 or Meena 26" She added one more piece of vital information "Meena is not 27 years old"
To add to the confusion, Mr. Tito was told by a neighbour that one of the sister always lies and the other two always speak the truth. Can you help him find the ages?
Labels: friday special, logic, puzzle
posted by Rajesh Lal at
9:39 AM
20 Comments:
Poor Mr. Tito. Why does he get stuck with these routes?
This way, Tito will never be able to complete his data for census.
Somebody help him
Why would the girls with stupid names be so vague anyway. Why do they like to torture Mr. Tito like this? So cruel. Any ways, the neighbor was lying and the girls are all 7
I think that Dika is 25, Meena is 26 and Ina is 27. Meena is the one who is lying.
very stupid name of the girls , but they seems to be very smart in logic, can't figure out the puzzle yet
Ina said "All of us are above 24 years of age, Dika is the youngest, and ofcourse I am the eldest."
"The difference between Dika's age and mine is three years and the sum of my age and Ina's age is two more that twice Dika's age" told mathematician Meena. I am eldest if and only if Dika is not the youngest, she added.
Dika was more "clear" than others , she said "Meena is elder to me" and "Either I am 24 years old or Ina 25 or Meena 26" She added one more piece of vital information "Meena is not 27 years old"
Ina gives very little information so I worked on the other two to see if their stories lined up. I they didn't, then Ina would be telling the truth. I did find that that Dika and Meena 's stories lined up as follows
I = Ina
M = Meena
D = Dika
Dika gives three age option
D = 24
I = 25
M = 26
Meena gives the following formula
M-D = 3 or D-M =3
and
M + I = (2 x D) + 2
Meena age is correct making
Meena 26
Dika 23
Ina (the liar) 21
And you can see that Meena is the oldest and Dika is not the youngest which was the other condition.
O.K. spectatcular, now who's right?
I = Ina
M = Meena
D = Dika
--M is NOT lying because of the statement:
"M is eldest if and only if D is NOT the youngest"
--for M to lie:
1. if D is youngest, M is eldest (this will make I a liar)
2. if D is Not the youngest, M is Not the oldest.(this again make I a liar)
--D is not lying because of the statement "M is older than D"
--for D to lie:
1. D is older than M.(this will make I a Liar)
SO, I agree with Gorro;
BTW, Ina should be 22.
M = meena
d = dika
i = ina
i: 24 <(or = to) d < m < i
M: |M-D| = 3 and M + I = 2D +2 and I < M IFF (if and only if) I < D
D: M > D and M = 26, or D = 24 or I is = 25
first substitiute D for 24 in |m-d|= 3 making m = 27 or 23 and M can not equal 27
then sub M for 26 making d = 23, 29 and since I staes that M > D and so does d then d cannot = 29
next sub 25 for i in M + I = 2D +2
making m = 2D - 23 sub that in for m in |m-d| = 3 and you get d = 26, 20
the possible answers so far are m = 26, or M = 20 and d is 23
if M is 26, d is 23, then I is 22
if m is 20, d is 23, then i is 28
now if m < D < I then I is wrong... and also M is < d then D is wrong making m not equal to 20
if m is 26 then I < D < M then I is wrong and both D and M are right
making the only possible answers:
Meena: 26
Dika: 23
Ima: 22
Trust me... this is the solution
The facts (mathematically):
Ina:
Fact 1: 24 is less than Dika is less than Meena is less than Ina
Meena:
Fact 1: |Meena-Dika|=3
Fact 2: Meena+Ina=2*Dika+2
Fact 3: Meena is less than Ina,Dika iff Dika is less than Ina,Meena
Dika:
Fact 1: Meena is greater than Dika
Fact 2: Dika=24 OR Ina=25 OR Meena=26
Fact 3: Meena|=27
Stranger:
Fact 1: One sister lies and two always tell the truth
Assumption 1: Stranger is telling the truth
Assumption 2: Age differences are measured ONLY in years
There are 3 scenarios:
Scenario 1: Ina, Meena tell truth
Fact 1 from Ina & Fact 3 from Meena contradict each other.
One of them is lying. Therefore, Dika is telling the truth.
Scenario 2: Ina, Dika tell truth
Under this scenario, there is one and only one possible solution:
Ina: 27
Meena: 26
Dika: 25
Scenario 3: Meena, Dika tell truth
In order for Fact 1 from Meena to be true, given Facts 2 & 3 from Dika, Dika cannot be 24.
Therefore (Fact 2 from Dika), either Ina is 25 or Meena is 26.
If Ina is 25, then, given all criteria from both parties:
Ina: 25
Meena: 29
Dika: 26
But, this contradicts Fact 3 from Meena.
If Meena is 26, then, given all criteria from both parties:
Ina: 22
Meena: 26
Dika: 23
But, this also contradicts Fact 3 from Meena.
THEREFORE, Ina & Dika are telling the truth, and Meena is lying.
Ina: 27
Meena: 26
Dika: 25
This is the only possible solution.
New genius -> Jeremy :)
Where is daniel btw
i mean
New genius -> Jesse
Poor poor Mr. Tito
but what is wrong with jesse's explanation is that they did not account for Dika's age - meena's age = 3 which is another possibility because the question states that the difference of meena and dika's age is 3 that could mean m-d = 3 or d-m = 3
also in the question ... fact 3 for meena say that meena is older than ina and dike iff (if and only if) dika is older than ina and younger than meena....
it states that meena is eldest if and only iff dika is NOT I REPEAT NOT the youngest
jeremy is right. i came up with the same answer the same way.
If Jesse's conclusion of Meena's account is false, the facts of Meena should not be hold.
Jesse's conclusion states that Meena can't be 26, Dika 23 and Ina 22 because that would contradict fact 3 from Meena - but why would it? Fact three states "I am eldest if and only if Dika is not the youngest." If Meena is 26, Dika is 23 and Ina 22, Meena would be eldest and Dika would NOT be youngest. No conflict. 26, 23 and 22 was my answer.
M=26
D=23
I=22
Conclusion, is that.
Damn this job. I'm quitting!
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