“Life’s funny”, said an old friend when I bumped into him the other day. “Listen to this, I was born in March, yet I celebrate my birthday in August, and last February I married my mother”.
He was born in the month of August in a town named March, became a priest and married his widowed mother to her second husband in February (the month).
The most impressive boundary’s not a wall. It’s not a manufactured thing at all. Moving towards it won’t reduce the gap and nothing marks its presence on a map.
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 piano. The word piano has five letters, and the scale on the piano is A through G, seven letters. The piano keys don’t have locks and playing piano requires you to keep time (but with a metronome, not a clock).