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.
An apple. They fall off trees and can be sweet or bitter depending on the type of apple. Most people buy apples, but you can get a free one if you have an apple tree. In olden days apples were used to throw at a person you loved, and in 2013 the company, Apple, pushed past Exxon Mobile to have the largest market capitalization in the United States.
King Ferdinand has no immediate living relatives and decides to hold a contest to find a worthy successor when he dies. He gives a seed to every contestant and explains that the person with the healthiest and most beautiful plant will win the throne.
When the final day of the contest arrives, the king finds hundreds of plants of all shapes and sizes. However, he ignores them and awards the throne to a girl holding a pot with only moist dirt.
King Ferdinand was a kind and trusting man and wanted to be sure he found an honest heir. He gave small pebbles to all the contestants, claiming they were seeds. Therefore, any contestant with a plant had switched their “seed” in order to win. Everyone but the girl had been dishonest.
9pm (or 21:00). There are 12 hours between 1pm and 1am, so 6 hours after 1am is halfway. 6 hours + 1pm equals 7pm. In order for 7pm to be 2 hours behind the current time, it must be 9pm.
What three or four-letter word belongs between the word on the left and the word on the right so that the first and second, and second and third words form a compound word or phrase?
For example: FOOT _ _ _ _ PARK would be BALL, or FOOTBALL and BALL PARK.
1. FALL _ _ _ CROP
2. KNEE _ _ _ SIZE
3. BOARD _ _ _ _ WAY