### Brain Teasers

# Water in 4 Jugs

You have four jugs:

A: 10-liter jug, filled with water

B: 10-liter jug, filled with water

C: 10-liter jug, empty

D: 9-liter jug, empty

Your objective is to end up having 1 liter in any 10-liter jug and 4 liters in 9-liter jug.

You have nothing else at your disposal and you can not measure using eye or shape of jugs.

Also water can only be transferred between jugs and not dumped out from any of the jugs.

A: 10-liter jug, filled with water

B: 10-liter jug, filled with water

C: 10-liter jug, empty

D: 9-liter jug, empty

Your objective is to end up having 1 liter in any 10-liter jug and 4 liters in 9-liter jug.

You have nothing else at your disposal and you can not measure using eye or shape of jugs.

Also water can only be transferred between jugs and not dumped out from any of the jugs.

### Hint

Not much of a hint, but it can be solved in 20 steps.### Answer

If we label jugs as stated in problem , ABCD, with 9-liter jug being D, problem can be solved in 20 steps, as shown below. Each step is shown in one row, where line start with number of step, followed by information from what jug we poured water into what jug, and how much ... ie. A -> (9) -> D means we poured 9 liters of water from jug A (being 1st 10-liter jug) to jug D (being 9-liter jug). Finally in row we show how much water we have in each jug after performed this step.---------------------------------

#s From-Qty-To A B C D

---------------------------------

0: = 10 10 0 0

1: A ->( 9)-> D = 1 10 0 9

2: D ->( 9)-> C = 1 10 9 0

3: A ->( 1)-> D = 0 10 9 1

4: B ->( 8)-> D = 0 2 9 9

5: D ->( 9)-> A = 9 2 9 0

6: A ->( 1)-> C = 8 2 10 0

7: B ->( 2)-> D = 8 0 10 2

8: C ->( 7)-> D = 8 0 3 9

9: D ->( 2)-> A = 10 0 3 7

10: D ->( 7)-> B = 10 7 3 0

11: A ->( 9)-> D = 1 7 3 9

12: A ->( 1)-> C = 0 7 4 9

13: D ->( 9)-> A = 9 7 4 0

14: A ->( 3)-> B = 6 10 4 0

15: B ->( 9)-> D = 6 1 4 9

16: B ->( 1)-> C = 6 0 5 9

17: D ->( 4)-> A = 10 0 5 5

18: D ->( 5)-> B = 10 5 5 0

19: A ->( 9)-> D = 1 5 5 9

20: D ->( 5)-> B = 1 10 5 4

After 20th step we end up with 1 liter in first 10-liter jug (A), and 4 liters in 9-liter jug (D), as requested in problem.

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