A GAS PLANET THATS OFF IN THE DISTANCE ONLY RECENTLY THEY FOUND MY RINGS IN EXISTENCE IM BLUE AND COLD AND FAR AWAY PEOPLE SAY IM NY BECAUSE I SPIN SIDEWA RIDDLES WITH ANSWERS TO SOLVE - PUZZLES & BRAIN TEASERS

The wind goes right through them! Did you answer this riddle correctly?
YES  NO  

Cachoo (cashew) nuts. Did you answer this riddle correctly?
YES  NO  

You have a racing pulse and a running nose. Did you answer this riddle correctly?
YES  NO  

True. You come down with a cold, never up. Did you answer this riddle correctly?
YES  NO  

Europe Did you answer this riddle correctly?
YES  NO  

Decemburrrr. Did you answer this riddle correctly?
YES  NO  

A dreidel. Did you answer this riddle correctly?
YES  NO  

I am a dreidel. Did you answer this riddle correctly?
YES  NO  

Hot chocolate Did you answer this riddle correctly?
YES  NO  

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

Prince:
3
6
12
18
24
30
36
42
48
54
60 Did you answer this riddle correctly?
YES  NO  

Repeat...Pete and repeat went fishing. Pete fell of the boat. Who was left? (keeps continuing because you are saying repeat) Did you answer this riddle correctly?
YES  NO  

Refrigerator Did you answer this riddle correctly?
YES  NO  

Ring a around the roses! Did you answer this riddle correctly?
YES  NO  

Roses Did you answer this riddle correctly?
YES  NO  

The Fridge Did you answer this riddle correctly?
YES  NO