There’s a whole set of problems about pouring water from one glass or jug to another. To make it more fun, let’s try lemonade. Warning: these problems are kind of hard. You have to figure out a way to draw them and keep track.
The rules are like this. You start with lemonade all in one or glass, and just by pouring from one glass to another, you divide the lemonade into certain volumes. Every time you pour from one glass to another, you have to pour as much as you can without spilling. So say you pour from a full 8-ounce glass into an empty 3-ounce glass. When you finish pouring, you have 5 ounces in the first glass and 3 in the second.
1. Okay, first problem. You have a full 7-ounce glass, an empty 4-ounce glass, and an empty 3-ounce glass. Pour from one to another until you have 3 ounces, 2 ounces, and 2 ounces. (I worked and worked on this one, and I finally got it in 7 pours.)
2. Second problem. In this one you can throw any leftover lemonade down the sink, and you can also refill any glass from the lemonade pitcher in the fridge. (But you don’t have any other glasses: you can’t pour, say, one ounce at a time into a third glass we don’t know about.) Okay, you have a 4-ounce glass and a 5-ounce glass. How can you measure out exactly 2 ounces? (For this one I filled a glass twice and emptied one down the sink once. I poured from one glass to another three times, I think.)
If you google “water-pouring problem,” you can find more of these. There are even some animations if you have Java. See what you can figure out, and then come back and tell me!
