I am the owner of a pet store. If I put in one canary per cage, I have one bird too many. If I put in two canaries per cage, I have one cage too many. How many cages and canaries do I have?
If you put one canary in each cage, you have an extra bird without a cage. However, if you put two canaries in each cage then you have two canaries in the first cage, two canaries in the second cage and an extra cage.
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.
Each letter represents a different digit. Any digit can be used, but zero can never start a word. Given W = 2 and R = 6, what do the rest of the letters represent?
Noah and Emma, track stars with superb hearing, ran as fast as they could to catch up to the ice cream truck in the next town over. They averaged 6 miles per hour, then rested to enjoy their ice cream. They averaged 4 miles per hour over the same distance on the way back. Not counting the time they rested, what was their average speed?
4.8 miles per hour. 5 mph is tempting, but incorrect. Pick any distance, say 12 miles there and 12 miles back. They take two hours to cover the first 12 miles and three hours to cover the return trip. In 5 hours they covered 24 miles which is an overall average of 4.8 miles per hour.