The Mad Veterinarian
A mad veterinarian has created three animal transmogrifying machines:
Machine I: Place a cat in the input bin. Press the Go button. Whirrr….Bing!
Open the output bin to find 2 dogs and 5 mice.
Machine II: Place a dog in the input bin. Press the Start button. Whirr….Thud…Bing!
Open the output bin to find 3 cats and 3 mice.
Machine III: Place a mouse in the input bin. Press the Run button. Whirrrr….Buzz…Ding!
Open the output bin to find a cat and a dog.
Note: each machine can also operate in reverse! (i.e., if you have 2 dogs and 5 mice, then you
can convert them into 1 cat)
Question 1: The mad veterinarian has handed you 6 mice and expects you to convert them into
only 4 dogs. Can you do it?
Question 2: Can you convert 3 cats to 7 mice?
Question 3: Can you convert 1 cat to 7 mice?
Observations:
Representation of Problem (algebraic):
Other questions to ponder:
1. Can you convert 1 cat into a pack of dogs, with no mice or cats left over?
2. How many mice can be created from a single cat?
3. What is the smallest number of cats that can be turned into just dogs?
Extension: What about 4 machines? These machines also operate in reverse.
Machine I: converts 1 cat to one dog and two mice.
Machine II: converts 1 dog into a mouse and 3 rabbits
Machine III: converts 1 mouse into 2 cats and 3 rabbits
Machine IV: converts 1 rabbit into 1 cat and 5 dogs
The mad veterinarian has handed you three cats, and expects you to convert them into four mice.
Can you do it?
Website applet: http://www.bumblebeagle.org/madvet/index.html