We have 16 tanks in a 4x4 grid.
+--+--+--+--+
|1 |2 |3 |4 |
+--+--+--+--+
|5 |6 |7 |8 |
+--+--+--+--+
|9 |10|11|12|
+--+--+--+--+
|13|14|15|16|
+--+--+--+--+
All the tanks are empty, except the first one, which is filled. We'd like to drain it. If you drain the water outside of the tank system, certain baby animals will be very sad, but draining the water from one tank to another is alright.
There is a door between each pair of adjacent tanks (but no diagonal connections). If you open the door between two tanks, the water levels will instantaneously equalize. What's the most you can drain out of the first tank?
1) Equalize tanks 1, 2, 3, and 4. Each is filled to 1/4.
2) Equalize tanks 1, 5, 6, 7, and 8. Each is filled to 1/20.
3) Equalize tanks 1, 5, 9, 10, 11, and 12. Each is filled to 1/60.
4) Equalize tanks 1, 5, 9, 13, 14 ,15, and 16. Each is filled with 1/140, or ~0.714%. Tank 1 has been drained of ~99.286% of its water.
Somehow I'm guessing we can do even better.
EDIT: Actually, I'm beginning to suspect that this might be the limit, as I've now come up with it several different ways. No idea what the math behind it would be, though...
Edited on October 14, 2013, 9:40 pm
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Posted by Jyqm
on 2013-10-14 21:21:19 |
More improvement
