Find the number of ordered pairs of positive integer solutions $(m, n)$ to the equation $20m + 12n = 2012$.
Soda is sold in packs of $6$, $12$ and $24$ cans. What is the minimum number of packs needed to buy exactly $90$ cans of soda?
Joe wants to measure $6$ liter water using just two containers whose capacities are $27$ liters and $15$ liters, respectively. Can you help him?
A class collects $50$ dollars to buy flowers for a classmate who is in the hospital. Roses cost $3$ dollars each, and carnations cost $2$ dollars each. No other flowers are to be used. How many different bouquets could be purchased for exactly $50$ dollars?
Of the pairs of positive integers $(x, y)$ that satisfies $3x+7y=188$, which ordered pair has the least positive difference $x-y$?