The sensors have led you to the origin of the distress signal: yet another handheld device, just like the one the Elves gave you. However, you don't see
any Elves around; instead, the device is surrounded by elephants! They must have gotten lost in these tunnels, and one of the elephants apparently
You need to get the elephants out of here, quickly. Your device estimates that you have 30 minutes before the volcano erupts, so you don't have time to
All of the valves begin closed. You start at valve AA, but it must be damaged or jammed or something: its flow rate is 0, so there's no point in opening
it. However, you could spend one minute moving to valve BB and another minute opening it; doing so would release pressure during the remaining 28
minutes at a flow rate of 13, a total eventual pressure release of 28 * 13 = 364. Then, you could spend your third minute moving to valve CC and your
fourth minute opening it, providing an additional 26 minutes of eventual pressure release at a flow rate of 2, or 52 total pressure released by valve
Making your way through the tunnels like this, you could probably open many or all of the valves by the time 30 minutes have elapsed. However, you need
to release as much pressure as possible, so you'll need to be methodical. Instead, consider this approach:
You're worried that even with an optimal approach, the pressure released won't be enough. What if you got one of the elephants to help you?
It would take you 4 minutes to teach an elephant how to open the right valves in the right order, leaving you with only 26 minutes to actually execute
your plan. Would having two of you working together be better, even if it means having less time? (Assume that you teach the elephant before opening any
valves yourself, giving you both the same full 26 minutes.)
In the example above, you could teach the elephant to help you as follows:
== Minute 1 ==
No valves are open.
You move to valve II.
The elephant moves to valve DD.
== Minute 2 ==
No valves are open.
You move to valve JJ.
The elephant opens valve DD.
== Minute 3 ==
Valve DD is open, releasing 20 pressure.
You open valve JJ.
The elephant moves to valve EE.
== Minute 4 ==
Valves DD and JJ are open, releasing 41 pressure.
You move to valve II.
The elephant moves to valve FF.
== Minute 5 ==
Valves DD and JJ are open, releasing 41 pressure.
You move to valve AA.
The elephant moves to valve GG.
== Minute 6 ==
Valves DD and JJ are open, releasing 41 pressure.
You move to valve BB.
The elephant moves to valve HH.
== Minute 7 ==
Valves DD and JJ are open, releasing 41 pressure.
You open valve BB.
The elephant opens valve HH.
== Minute 8 ==
Valves BB, DD, HH, and JJ are open, releasing 76 pressure.
You move to valve CC.
The elephant moves to valve GG.
== Minute 9 ==
Valves BB, DD, HH, and JJ are open, releasing 76 pressure.
You open valve CC.
The elephant moves to valve FF.
== Minute 10 ==
Valves BB, CC, DD, HH, and JJ are open, releasing 78 pressure.
The elephant moves to valve EE.
== Minute 11 ==
Valves BB, CC, DD, HH, and JJ are open, releasing 78 pressure.
The elephant opens valve EE.
(At this point, all valves are open.)
== Minute 12 ==
Valves BB, CC, DD, EE, HH, and JJ are open, releasing 81 pressure.
