“The three witches in Hamlet can brew any potion provided they have the right ingredients. Suppose that five ingredients are necessary in making a health potion: eye of newt (eon), toe of frog (tof), wool of bat (wob), adder’s fork (af), and tooth of wolf (tow). Four reactions can occur between these ingredients:
4 eon + 2 wob = 3 af + 4 tow
3 tow + 1 tof = 2 eon
1 wob + 2 af = 1 tof
4 tof + 7 tow + 2 af = 1 health potion
Assuming you can control the order of reactions, write a program that can calculate the maximum number of health potions one can brew with a given amount of ingredients. Here is example output:
If I have 34 eon, 59 tof, 20 wob, 5 af, and 20 tow, I can make seven health potions.”

Excerpt From: Ophir Frieder, Gideon Frieder, and David Grossman. “Computer Science Programming Basics with Ruby.” iBooks.