Suppose a small bank has one teller and customer transactions take 10 minutes on average. With 5.8 customers arriving per hour, what is the expected wait time? What would it be if you added a second teller?
Noreen doesn’t have a driver’s license and goes the wrong way on a one-way street, then turns left at a corner with a “No left turns” sign. A policeman sees her but does nothing. Why?
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 moon. The moon has been around for quite some time, but there’s a “new” moon every month or so. A Blue moon is a rare event. The moon is a body of rock, so it’s never empty, but we do see what we call a full moon some nights. And the moon’s gravity “pulls” on the ocean to create low and high tides, but it doesn’t push anyone around because it’s a friendly fellah.