Solution, part one
Solution, part two
I believe you can do this in as little as 8 pours. The trick is to think of the 4L jug as measuring 8L, because 9-8=1, and 8-7=1. Once you get the two jugs with 1L, the remaining liquid is easily distributed using the 2L jug.
You start with 9-0-0-0
1. Fill the 4L jug: 5-0-4-0
2. Transfer that to the 7L jug: 5-4-0-0
3. Fill the 4L jug again from the 9L jug: 1-4-4-0
4. Fill the 7L jug from the 4L jug: 1-7-1-0
5. Fill the 2L jug from the 7: 1-5-1-2
6. Pour the 2L into the 9: 3-5-1-0
7. Fill the 2L from the 7 again: 3-3-1-2
8. Pour the 2L into the 4L: 3-3-3-0
That said, good luck ending up with exactly 9L of liquid after five pours to the brim!
Is there a way to do this in fewer pours (without using a marker)?
I was first stumped by how to get two jugs each filled with 1 liter of water. I tried doing it in my head without much luck.
So I went the slow methodical approach of writing every step on paper. I even had to figure out how to display my steps since the jugs have numbers associated with them for their total volume (2,4,7,9) and each step changed the amount of water in a vessel.
I also realized that adding two arrows ⬇️↘️ helped to show when only part of the water in a vessel was poured into another.
When I realized I could get 4 liters into 2 vessels and then end up with the “second 1 liter” if I filled up the 7 liter vessel, it was pretty much solved.
I don’t think I duplicated any steps with my approach, just took a longer path.
But asking can I do it in fewer steps should have been the next question.
I guess the next questions after that is
What is the volume ratio of vessels required to have 5 liters in 3 vessels? 7 liters in 3 vessels? n liters in 3 vessels?
Does the ratio need to change if you have even liters in 3 vessels? I.e. 4 liters in 3 vessels? 8 liters in 3 vessels?
Needing to get 1L volumes didn't occur to me until after I saw your solution. At first I was going for 3L volumes, which you can get by pouring 9 -> 4+2, or 7->4. My first solution was this:
1. Pour the 9L into both the 4L and 2L, leaving 3L in the 9L jug: 3-0-4-2
2. Use a marker or piece of tape, or your finger, to mark the 3L level on the 9L jug:
3. Pour the remaining 3L into the 7L jug: 0-3-4-2
4. Pour the 2L and 4L back into the 9L jug (giving 6L): 6-3-0-0
5. Pour 3L of water (down to the mark) back into the 4L jug, thus leaving 3L in the 9L jug: 3-3-3-0
That's not technically against the rules, but I thought it was probably against the spirit of the puzzle. So I read your solution and thought about how to get 1L (which you need to in order to solve), and tried again.