Question

given: 1 pail = 4 liters
1 pail = 9 liters

You are going to the river to fetch water. How could you carry 6 liters of water using only this two pails?

note: pails have no permanent calibration.

Answer 1

Think of the equation

9x+4y=1

Look for x and y to satisfy the above equation, obviously one of them has to be negative. This will give you an idea how to go about getting the answer.

If you need a systematic way to solve it, look up diophantine equations.

Answer 2

pail 1 pail 2
9 0
5 4
5 0
1 4
1 0
0 1
9 1
6 4

Answer 3

Sorry, the above equation should have read:
9x+4y=6
which makes
9*(2)-4*(3)=6 (using Gow's results)

Answer 4

my solution is:

(1) the 2 pails have no calibration

(2) solve:
9 -4 =5
5-4 = 1

(3) now that you have remaining 1 liter of water.

(4) put that 1 liter of water to 4 liter-capacity pail

(5) the 9 liter-capacity pail has no content

(6) full it with water

(7) now, since the 4 liter-capacity pail has 1 liter inside, you need only 3 liter to full it.

(8) solve:
9-3 = 6 ; final answer