### Brain Teasers

# Water From 3 Jugs Into Two Pools

You have:

- two 10-liter jugs, full of water

- one 9-liter jug, empty

- two large pools, empty

Your objective is to end up having 4 liters of water in each pool, and one liter of water in the 9-liter jug.

You have nothing else at your disposal and you can not measure using eye or shape of jugs. You can not pour water from pools, only into them.

- two 10-liter jugs, full of water

- one 9-liter jug, empty

- two large pools, empty

Your objective is to end up having 4 liters of water in each pool, and one liter of water in the 9-liter jug.

You have nothing else at your disposal and you can not measure using eye or shape of jugs. You can not pour water from pools, only into them.

### Hint

This needs 29 steps to fill two pools with 4-liters, and an additional 4 steps to get 1 liter in the 9-liter jug, for a total of 33 steps.### Answer

Label the 10-liter jugs as A and B, the 9-liter jug as C, and the two pools as Pa and Pb. The problem can be solved in 33 steps, as shown below. Each step is shown in one row, starting with the step number, followed by the jug we poured water from, then the quantity of water, then the jug/pool we poured water into... i.e. A ->( 1)-> Pb means we poured 1 liter of water from jug A (being 1st 10-liter jug) to pool Pb (being 2nd pool). Finally in the row we show how much water we have in each jug/pool after performing this step.------------------------------------

#: From -> Qty -> To = A B C Pa Pb

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

0: _____________ = 10 10 0 0 0

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

2: A ->( 1)-> Pa = 0 10 9 1 0

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

4: B ->( 9)-> C = 9 1 9 1 0

5: B ->( 1)-> Pa = 9 0 9 2 0

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

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

8: A ->( 9)-> C = 1 8 9 2 0

9: A ->( 1)-> Pa = 0 8 9 3 0

10: C ->( 9)-> A = 9 8 0 3 0

11: A ->( 2)-> B = 7 10 0 3 0

12: B ->( 9)-> C = 7 1 9 3 0

13: B ->( 1)-> Pa = 7 0 9 4 0

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

15: C ->( 6)-> B = 10 6 0 4 0

16: A ->( 9)-> C = 1 6 9 4 0

17: A ->( 1)-> Pb = 0 6 9 4 1

18: C ->( 9)-> A = 9 6 0 4 1

19: A ->( 4)-> B = 5 10 0 4 1

20: B ->( 9)-> C = 5 1 9 4 1

21: B ->( 1)-> Pb = 5 0 9 4 2

22: C ->( 5)-> A = 10 0 4 4 2

23: C ->( 4)-> B = 10 4 0 4 2

24: A ->( 9)-> C = 1 4 9 4 2

25: A ->( 1)-> Pb = 0 4 9 4 3

26: C ->( 9)-> A = 9 4 0 4 3

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

28: B ->( 9)-> C = 3 1 9 4 3

29: B ->( 1)-> Pb = 3 0 9 4 4

30: C ->( 7)-> A = 10 0 2 4 4

31: C ->( 2)-> B = 10 2 0 4 4

32: A ->( 9)-> C = 1 2 9 4 4

33: C ->( 8)-> B = 1 10 1 4 4

After the 33rd step we end up with 4 liters in each pool (Pa and Pb), and 1 liter in the 9-liter jug (C), as requested in the problem.

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## Comments

oldy but a goody

I think I got the answer but I haven't got a clue from the explanation. You keep adding water 1L at a time, filling the 10L to the top with the other 10L bottle, and using the full 10L to put in the 9L, right?

I used to play i game like this in grade school, but a little less advanced, this one was esay and iu accually completed it in 30STEPS not 33, and up with 4L in pA and pB, 3L in A, 0L in B, and 9L in C.(20L). After leveling it off the first time with 2steps, repetively transfer the 9L in C to B and add 1L from A to B, add 9L from B to C, put remaining 1L in B in pA.(you will do this 7 times[7x4steps = 28+2steps =30 STEPS]). THE GAME I PLAYED IN GRAMMER SCHOOL WAS TO SEE WHO DID IN IN THE LEAST AMOUNT OF STEPS, SO LOOKS LIKE I WON

I think that solution under 33 moves for this problem does not exists, Smart . I assume you were reffering to another problem, one where target is to end up with 9L in jug C. Actually, that one can be solved in 29 moves

Tedious but fun! Can't believe I actually went through all 33 steps. Wrote my answer in a way I found clearer to read though.

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