A princess is as old as the prince will be when the princess is twice the age that the prince was when the princess’s age was half the sum of their present ages.
This one took a while to figure out and there are numerous valid ways of finding the answer.
Here is the solution I came up with
I created the following table from the riddle:
Current
Future
Past
Princess
x
2z
(x+y)/2
Prince
y
x
z
I then created three equations, since the difference in their age will always be the same. d = the difference in ages x – y = d 2z – x = d x/2 + y/2 – z = d
I then created a matrix and solved it using row reduction.
x
y
z
1
-1
0
d
-1
0
2
d
.5
.5
-1
d
It reduced to:
x
y
z
1
0
0
4d
0
1
0
3d
0
0
1
5d/2
This means that you can pick any difference you want (an even one presumably because you want integer ages). Princess age: 4d Prince age: 3d
Ages that work
Princess
Prince
4
3
8
6
16
12
24
18
32
24
40
30
48
36
56
42
64
48
72
54
80
60
To see other solutions check out the comments from when I posted this on my blog.
My first is twice in apple but not once in tart. My second is in liver but not in heart. My third is in giant and also in ghost. Whole I’m best, when I am roast. What am I?
The next number in the series counts the previous numbers. Thus the first number is 1, which is one 1, or 11. To describe 11, you have two 1’s, or 21. Now you have one 2 and one 1, so the next number is 1211. The solution is to continue describing the previous number using only numbers.
You walk into a room and see a bed. On the bed there are two dogs, four cats, a giraffe, five cows and a duck. There are also three chickens flying above the bed. How many legs are on the floor?
Since all of the animals are on the bed and no other furniture is mentioned in the room, there are six legs on the floor. Four legs from the bed and your own two legs as you stand in the room, amazed that someone managed to get so many animals onto a bed. And the ceiling must be vaulted to fit a giraffe. Also, who’s on cleanup duty?
My first is in FLOWER and in ROSE My second is in FORK and well as HOSE My third is in CROCUS but not in GNOME My fourth is in RAKE never in HOME My fifth is in HOE and also in WEEDS My sixth is in SHEARS though not in SEEDS My seventh is in LADYBIRD not in CREATURE