i’m not sure where riddles should go, but since i took this from baldur’s gate II i’ll post this here.
i already have the answer but i don’t follow the logic. i’ll let you guys have a go at it before i post the answer and my confusion.
I think this one needs simple algebra. The trick is to write an eqaution for each fact given, and then solve it. Use F for princess’ current age and M for prince’s current age. To parse the sentance it’s easiest to read it backward.
“when the princess’ age was half the sum of their present age”
ie. when princess is a=(F+M)/2 years old
“when the princess is twice as old as the prince will be when the princess’ age was” a=(F+M)/2
ie. when princess is 2*(M+(a-F)) years old (since the prince’s age at that time will be as greater as it is now as the princess’ will be, and we know her current and then age)
ie. when princess is b=2*(M+F/2+M/2-F)=3M-F years old
“The princess is as old as the prince will be when the princess is” b=3M-F years old
ie. F=M+((3M-F)-F)=4M-2F (using same trick as before. This is her actual age, so we put F= at the start)
ie. F/4=M/3 rearanging to get M and F on opposite sides
We only have one equation here so we can’t establish the ages from that. But we can say which options are possible. Only 2 has the ages in this ratio.
Did I get it right? Does my explanation help?
The answer is #3, although #6 has a lot going for it.
Start with Princess= 40, Prince = 30
Princess is half the sum of their present ages
when Princess = 35, Prince = 25
doubling Prince’s age gives 50.
when Princess= 50, Prince = 40
I suppose if you want the logic mapped out, here’s one way:
Prince’s age now = P
Princess’s age now = S
First, if we assume the grammar to be correct, then the princess would have to be the older of the two, or else the average of their ages would be in the princess’s future, while the riddle uses the past tense.
When the princess’s age was half the sum of their current ages (P+S)/2, the Prince’s age was P-(S-(P+S)/2). Double this to get the future Princess’s age of 2(P-(S-(P+S)/2)). The Prince’s age at this time will be P+(2(P-(S-(P+S)/2))-S). If this is equal to the Princess’s age right now, then you have the correct answer.
So, if P+(2(P-(S-(P+S)/2))-S) = S, then the choice is true.
Starting with choice 1, we get:
P=20, S=30
20+(2(20-(30-(20+30)/2))-30)
20+(2(20-(30-(25))-30)
20+(2(20-5)-30)
20+(30-30)
20+0 = 20 != S
False.
Skip ahead to choice 3:
For P=30, S=40
30+(2(30-(40-(30+40)/2))-40)
30+(2(30-(40-(35))-40)
30+(2(30-(5))-40)
30+(50-40)
30+10 = 40 = S
True.
Okay, here goes. I’ll refer to the Prince and Princess’s present ages as M and F, respectively, as well as defining the following terms for simplicity:
D = the difference in their present ages (i.e. M - F)
T = the total of their present ages (i.e. M + F)
I’ll work the conditions backward and add derivative terms as required:
C[sub]1[/sub] : F[sub]1[/sub] = T / 2 (i.e. F[sub]1[/sub] is the age of the Princess when she was half as old as the present total)
C[sub]2[/sub] : M[sub]1[/sub] = F[sub]1[/sub] + D (i.e. the Prince’s age when the Princess was F[sub]1[/sub]. D never changes, regardless of their ages at any given time)
C[sub]3[/sub] : F[sub]2[/sub] = 2 * M[sub]1[/sub] (when the Princess was twice as old as the Prince was)
C[sub]4[/sub] : M[sub]2[/sub] = F[sub]2[/sub] + D (see C[sub]2[/sub])
C[sub]5[/sub] : F = M[sub]2[/sub] (i.e. the Princess is as old as the prince will be)
Using substitution:
F = M[sub]2[/sub]
F = F[sub]2[/sub] + D
F = (2 * M[sub]1[/sub]) + D
F = [2 * (F[sub]1[/sub] + D)] + D
F = [2 * (T / 2 + D)] + D
F = (T + 2 * D) + D
F = T + 3 * D
F = M + F + 3 * D
Therefore:
0 = M + 3 * D
Therefore:
M = (-3) * D
Therefore, the Prince’s current age is equal to negative three times the difference in their ages. From the given answers, only (3) conforms:
M = 30, F = 40, D = -10
30 = (-3) * (-10)
By filling in the values of the original question: (A princess is as old as the prince will be when the princess is twice as old as the prince was when the princess’ age was half the sum of their present age.)
M = 30, F = 40, T = 70
Five years ago, the Princess was half the current total:
M = 25, F = 35
When the Princess is twice the age of the Prince at that point:
M = 40, F = 50
When the Princess is as old as the Prince will be at that point:
M = 30, F = 40, which matches the initial conditions.
I’m sure there’s an easier way to resolve this, including using (M-F) instead of D and (M+F) instead of T, but there you go. I imagine other solutions might be possible, i.e. if the ages of the characters were doubled.
Your math looks ok, but then you got your F and M switched around at the last step. The choice that fits your numbers would be 3, which is the same as what Bryan Ekers and I got.
:smack: yep, I just noticed that.
If I’d have spotted the grammar thing I’d have caught that - that was inspired of you 
See, this is why math sucks…
Algebra being invented hasn’t taken anything away from you. If you want to sit gawping like a stunned seabird, or solving the riddle by trial and error, you can.
It’s just that the extra option of finding the answer in an easy and systematic way is also possible, which is what I plumped for.
the answer, as had been found is, ’ 3. The prince is 30 and the princess is 40. ’
thanks for the reasoning behind the answer, i understand it now.
this is embarrassing, but the way i had read it was - (it’s either 1 or 3, i picked 1 first)
when the princess’ age was half the sum of their present age.
([20+30]/2=25 . where the princess age is 25 the prince would be 15)
when the princess is twice as old as the prince was
(the prince was 15, so twice as old for the princess would be 30)
A princess is as old as the prince will be
(so the princess is 30 as the prince will be 30 eventually…)
i see i had messed up ‘the prince will be’ part.
In fact, you can multiply the ages by any number, and it’ll still work. All we know is that the prince is three fourths the age of the princess. The sentence in the riddle amounts to only one equation (admittedly a really ugly one) in two variables. Therefore, the correct answer is 6: I surely don’t know.
What happens in the game if you say you don’t know?
The question sounds somewhat ambiguous - it asks which of these could be true. 3 can be. 1,2,4,5 can’t be. Normally the last option would be ‘insuficient information’ but since the question is ‘could’ that translates to ‘yes, could be’. I’m guessing it’s just a ‘I can’t work it out’ option.
Come to think of it, depending on how you define ‘old’ and ‘age’ they actually could be the same age. Eg. prince=12 months, princess=16 months, so the prince is the 3/4 as old, but they are the same age (1 year old). It depends on the wording in the question, and I don’t think this is the intended answer. But nobody else was as pedactic as me, woohoo!
my curiousity piqued, i looked up the cheat codes and checked. Shade got it right, when i chose 6 he reproved me for not trying, then went on to give me the second easy riddle which was what i got for giving the wrong answer. had i given the correct answer on the first question i would get more experience points.