# Prince Age Riddle

Riddle: 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. What are their ages?

The answer: Riddles have always been a popular form of brain training fun.
You may be seen the “Prince Age” a riddle on the Internet or on social media and have been struggling with its answer for a while.

#### Prince Age Riddle

This riddle has been around for some time on internet platforms such as Instagram, Facebook, and WhatsApp, and many people still argue over what the answer might be, as there are many possibilities.

The answer to the Prince Age riddle is below.

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:
4
8
16
24
32
40
48
56
64
72
80

Prince:
3
6
12
18
24
30
36
42
48
54
60