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.
A red-house is made of red bricks, has a red wooden door and a red roof. A yellow-house is made of yellow bricks, has a yellow wooden door and a yellow roof. What is a green-house made of?
A windmill. The typical windmill, like the ones Don Quixote chased, have four vanes or sails. You might even say they look like wings. Windmills don’t have emotions, so they can’t laugh or cry. And since they don’t have actual wings, windmills don’t get off the ground. A well-oiled little bugger won’t make a peep.
The missing numbers are 4 and 9. The list is sorted alphabetically by the English spelling of the numbers, so four belongs after five and nine comes after fourteen.
During WWII, there was a bridge connecting Germany and Switzerland, and on the German side, there was a sentry tower with a guard in it. He would come out every three minutes to check on the bridge, and he had orders to turn back anyone who tried to get into Germany, and shoot anyone trying to escape without a pass. There was a woman who desperately needed to get into Switzerland, and she knew she didn’t have time to get a pass. It would take her at least six minutes to cross the bridge, but she managed to do it. How?
She walked on the bridge towards Switzerland for 3 minutes and just as the guard was about to come out, she turned around walking back to Germany. The guard saw her and asked for her pass but she didn’t have one and was sent back (or what the guard thought was back) to Switzerland. In her case it was the very country she wanted to go to.
