Let’s keep this discrete.
Today’s pod and blog are about one of the many facets of Discrete Mathematics.
Here are two solutions to the 3‑gallon/ 5‑gallon jug problem.
First Solution
The first solution is a 6‑step solution:
1. With two empty jugs, I would fill the 5‑gallon jug. Now the 5‑gallon jug now has 5 gallons of water.
2. I would pour the 5‑gallon jug into the 3‑gallon jug, which now means I have the 3‑gallon jug filled with 3 gallons of water and the 5‑gallon jug filled with 2 gallons of water.
3. Then I would pour out the 3‑gallon jug, which leaves me only two gallons of water in the 5‑gallon jug.
4. Then I would pour the two gallons of water from the 5‑gallon jug into the 3‑gallon bottle. Then I would have 2 gallons in the 3‑gallon bottle and an empty 5‑gallon jug.
5. Then I would fill the 5‑gallon jug completely full. That gives me 5 gallons of water in the 5‑gallon jug and 2 gallons of water in the 3‑gallon jug.
6. Then I would pour water from the 5‑gallon jug into the 3‑gallon jug. That gives me 3 gallons of water in the 3‑gallon jug and 4 gallons of water in the 5‑gallon jug. There are the 4 gallons that I need!
Second Solution
Here is the second solution:
1. With two empty jugs, I would fill the 3‑gallon jug with 3 gallons of water.
2. Then I would pour the 3 gallons of water into the 5‑gallon jug. Now the 3‑gallon jug has no water, and the 5‑gallon jug has 3 gallons of water.
3. Then I would fill the 3‑gallon jug. Now the 3‑gallon jug has 3 gallons of water, and the 5‑gallon jug has 3‑gallons of water.
4. Then I would pour the water from the 3‑gallon jug into the 5‑gallon jug. Now the 3‑gallon jug has 1 gallon of water, and the 5‑gallon jug has 5 gallons of water.
5. Then I would empty the 5‑gallon jug. Now the 3‑gallon jug has 1 gallon of water, and the 5‑gallon jug is empty.
6. Then I would pour the 1 gallon from the 3‑gallon jug into the 5‑gallon jug. Now the 3‑gallon jug is empty, and the 5‑gallon jug has 1 gallon.
7. Then I would fill the 3‑gallon jug full. Now the 3‑gallon jug has 3 gallons, and the 5‑gallon jug has 1 gallon.
8. Then I would pour the water from the 3‑gallon jug into the 5‑gallon jug. There are the 4 gallons that I need!!
How not to Die Hard
Mathologer has a great video here that creates a process for understanding how to solve this problem. This is great because technically, the method provides a way for one to solve any two-bucket problem, given that the two buckets are different sizes. Please check it out and have some fun with this!
Books
And if you are interested in learning more about Discrete Math, I want to recommend two of my absolute favorite college textbooks on Discrete Math. The first, titled Discrete Mathematics with Applications is one of the most straightforward college textbooks in this subject to understand. It is written by Dr. Susanna S. Epp. Dr. Epp is a Professor Emerita of Mathematical Sciences at DePaul University in Chicago. I bought a used version of this as an undergrad, and it became my favorite math bible.
The second book is Mathematics for Information Technology by Dr. Alfred Basta, Professor Nadine Basta, and Professor Stephon DeLong. Dr. Basta was my professor in my undergrad studies (Hi Dr. Basta!), and this book is really a fun read, full of puzzles and math problems, and as a math nerd, I found it enjoyable to the last page.
Finally, McClane is coming back next year! Until 2020, I’ll be catching up on all the Die Hard movies!
So, until next week, yippee ki-yay and carpe diem!