The Problem: Pouring problems


The most common two sizes for pouring problems use quantizes of 4 and 7, and 5 and 3. You can see in these pictures that with a few operations filling and emptying (or filling) the containers you can derive any value from 1 to 7 or 1 to 5.

Here we can see generating any value from 1 to 5 gallons, the shaded areas.

Similarly here you can see generating any value from 1 to 7 gallons.

So in terms of our example problems - to make the burrito you would flip both the four and seven-hour glasses over. When the four-minute timer runs our there are three minutes left in the seven-minute timer. Set the hour glass on its side (kind of cheating to stop the clock), insert the pizza, then set up the timer to measure three minutes.

The answer to the buckets problem is to first fill the three-gallon bucket up and use it to fill the five-gallon bucket with two pours. The first pour leaves three-gallons in the five-gallon bucket. During the second pour when the five-gallon bucket is full there is one-gallon left in the three-gallon bucket. Or you can do it using as illustrated pouring from the five-gallon bucket twice into the three-gallon bucket.