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.
Hans made a meandering journey from Paris to Roye. On the first day, he went half of the distance. On the second day, he went one third of the remaining distance. On the third day he went three quarters of the remaining distance. The next day he traveled half of the remaining distance and was left with 5 kilometers to get to Roye. How far was the entire journey?
Day 1 – 60 km (60 km remaining)
Day 2 – 20 km (40 km remaining)
Day 3 – 30 km (10 km remaining)
Day 4 – 5 km (5 km remaining)
Day 5 – 5 km (arrives in Roye)
Alfred is at the bank to cash his $200 check. He tells the cashier he would like some one dollar bills, ten times as many two dollar bills and the rest in fives.
How many of each denomination does the cashier need to give Alfred?
We know that in order to give the rest of the amount in fives, the sum of the one and two dollar bills needs to be divisible by five (i.e. end in 0 or 5).
If we start with a single one dollar bill, we’d need ten two dollar bills to satisfy the request, making $21. But we need a sum that is divisible by 5. So we keep going up, like so:
The moon. It has two sides, but on earth we only ever see one side. Man has been on the moon, but no one is there now. A full lunar eclipse is known as a blood moon, and the phrase “once in a blue moon” refers to something that rarely happens. Promising the moon is making an extravagant or impossible promise, and there’s a new moon once every lunar cycle.
I can be quick and then I’m deadly,
I am a rock, shell and bone medley.
If I was made into a man, I’d make people dream,
I gather in millions by ocean, sea and stream.
Sand. Quicksand is deadly (at least in movies). Sand is made up of rocks, shells and bones. The sandman visits you when you dream (again, according to legend, I’ve never seen him…) and there is plenty of sand in the oceans, seas and streams.