A black dog is sleeping in the middle of a black road that has no streetlights and there is no moon. A car coming down the road with its lights off steers around the dog. How did the driver know the dog was there?
Brandon was walking around at the carnival. A man called out from a booth and said, “If I can write your exact weight on this piece of paper, you have to pay me $50. If I can’t do it, I’ll pay you $50.”
Brandon checked the booth for a scale but saw nothing. He agreed. Since your weight can fluctuate by a pound or two, he decided that no matter what number the man wrote, he would just say he weighed a pound more or less. In the end, the man in the booth won the $50. How did he do it?
An apple. They fall off trees and can be sweet or bitter depending on the type of apple. Most people buy apples, but you can get a free one if you have an apple tree. In olden days apples were used to throw at a person you loved, and in 2013 the company, Apple, pushed past Exxon Mobile to have the largest market capitalization in the United States.
Ralph goes to the hardware store to buy something for his house. He asks the clerk how much one will cost and the clerk looks it up and tells him it will be $3. He asks about buying twelve and is told it will be $6. Two hundred will cost $9.
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.