# A thirsty king and his knights

The black king has spent his life fighting over this strange checkered land, the white king has finally been defeated and his troops have surrendered and pledged allegiance to him. Now he's not sure what to do with himself, he decides to have a drink. But he is a king! He can't just have any normal drink that some lowly pawn might have. He demands a drink of exactly 2 litres be delivered to him! As quickly as possible!

The knight on A7 is carrying a jug of capacity 7 litres, The knight on F1 is carrying a jug of capacity 11 litres. They both start empty. The black knight is a source of infinite water. The goal is to have 1 knight carrying exactly 2 litres of water and deliver it to the king.

Rules:

You are only allowed to entirely empty or fill the jugs, no pouring out half

You can move any piece in any order, you don't have to go W,B,W,B etc.

Knights move as knights and can only interact with each other when they are either horizontal or Vertical, they cannot interact if diagonal

The king can move as a normal king and interacts with the same rules as the knights

Filling or emptying a jug counts as a 'move'

Your task is to try and find the solution with the fewest moves
I have accepted an answer of 23 as I don't know of a way to do fewer but I haven't 'proved' this so feel free to try and improve upon it :)

• I suppose the pieces also have to be adjacent to each other when they interact? – Bass May 27 '18 at 19:31
• @Bass Yes they do – Jon.G May 28 '18 at 11:13

It's possible to do it in

23 moves

White Knight 1 (7 liter capacity) is W1
White Knight 2 (11 liter capacity) is W2
Black Knight (water source) is B

1. W1 to B5
2. W1 to C3
3. W2 to E3
4. W2 to C2
5. B to G6
6. B to F4
7. B to D3
8. W1 fills 7            W1 7 W2 0
9. W1 gives 7 to W2      W1 0 W2 7
10. W1 fills 7           W1 7 W2 7
11. W1 gives 4 to W2     W1 3 W2 11
12. W2 empties           W1 3 W2 0
13. W1 gives 3 to W2     W1 0 W2 3
14. W1 fills 7           W1 7 W2 3
15. W1 gives 7 to W2     W1 0 W2 10
16. W1 fills 7           W1 7 W2 10
17. W1 gives 1 to W2     W1 6 W2 11
18. W2 empties           W1 6 W2 0
19. W1 gives 6 to W2     W1 0 W2 6
20. W1 fills 7           W1 7 W2 6
21. W1 gives 5 to W2     W1 2 W2 11
22. W1 to A2
23. W1 dumps 2 liters of water on the King

• I didn't even think about moving the back knight... – Saeïdryl May 25 '18 at 14:37
• I think it makes notation clear if you call White Knight 1 (7 liter capacity) and White Knight 2 (11 liter capacity) J and K, or X and Y? – smci May 26 '18 at 10:33
• @smci or S and E (for Seven/Eleven) – Angew is no longer proud of SO May 26 '18 at 11:18

I can do it in

25 moves

Step-by-step :

3 moves to put Knight1 from A7 to G8
3 moves to put Knight2 from F1 to G7 (thanks hexomino)
Knight1 fills 7L
Knight1 gives Knight2 7L (7L total) (0L left)
Knight1 fills 7L
Knight1 gives Knight2 4L (11L total) (3L left)
Knight2 empty
Knight1 gives Knight2 3L (3L total) (0L left)
Knight1 fills 7L
Knight1 gives Knight2 7L (10L total) (0L left)
Knight1 fills 7L
Knight1 gives Knight2 1L (11L total) (6L left)
Knight2 empty
Knight1 gives Knight2 6L (6L total) (0L left)
Knight1 fills 7L
Knight1 gives Knight2 5L (11L total) (2 left)
4 moves to put Knight1 from G8 to A2 (or B1)
Knight1 gives 2L to the king
Total : 25 moves

• Couldn't you have the knight at f1 move to g7 instead (3 moves)? – hexomino May 25 '18 at 14:05