Imagine you are in a dark room with a locked door. All you have with you is a rope and a pencil. You can hear the rain outside, but there are no windows. How do you get out?
In addition to the two hands on the end of their arms, they also have three hands of cards. Another alternative could be handwriting, of which most people have one, but that could be added into the mix.
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?
Putting the information in a table makes it easier to solve. We’ll use A for Angie, B for Brenda, T for truth and F (false) for lying.
S
M
T
W
Th
F
S
A
T
F
F
F
T
T
T
B
T
T
T
T
F
F
F
To begin with, there aren’t any days where both of them told the truth and lied the day before, so we know one of them must be lying.
So we have two options, either Angel is lying or Brenda is.
Option 1. Angel is lying.
In order for this to be the case, she needs to be lying today and telling the truth yesterday, so we need two days in a row with T F. And if Brenda is telling the truth, she would need two days with F T. That means we’re looking for two days that have
Angie: T F
Brenda: F T
Option 2. Brenda is lying.
This is just the reverse of the above, so we need to find:
Angie: F T
Brenda: T F
The only day that matches either of the two options is Thursday, and it’s option 2. Brenda is the liar.