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.
The name ABRAHAM can be changed into a word for a primitive musical instrument by replacing each letter with a different letter. The repeated letters (A is this case) must be replaced with the same replacement letter in the new word.
Noon and midnight are both 12 o’clock and the Twelve Days of Christmas is a popular Christmas carol.
There are twelve face cards in a standard 52-card deck and twelve is the largest number with one syllable.
There are twelve steps in Alcoholics Anonymous, a troy pound is 12 ounces, there were 12 tribes of Israel and a popular movie was called, “Twelve Angry Men” (12 members of the jury). There are twelve function keys on your keyboard. F1 often shows a help screen and F5 reloads pages in your browser.
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It’s surprising how many times the number twelve shows up in our culture.
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