276 lines
8.2 KiB
Org Mode
276 lines
8.2 KiB
Org Mode
** --- Day 16: Proboscidea Volcanium ---
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The sensors have led you to the origin of the distress signal: yet
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another handheld device, just like the one the Elves gave you. However,
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you don't see any Elves around; instead, the device is surrounded by
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elephants! They must have gotten lost in these tunnels, and one of the
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elephants apparently figured out how to turn on the distress signal.
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The ground rumbles again, much stronger this time. What kind of cave is
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this, exactly? You scan the cave with your handheld device; it reports
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mostly igneous rock, some ash, pockets of pressurized gas, magma... this
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isn't just a cave, it's a volcano!
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You need to get the elephants out of here, quickly. Your device
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estimates that you have /30 minutes/ before the volcano erupts, so you
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don't have time to go back out the way you came in.
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You scan the cave for other options and discover a network of pipes and
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pressure-release /valves/. You aren't sure how such a system got into a
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volcano, but you don't have time to complain; your device produces a
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report (your puzzle input) of each valve's /flow rate/ if it were opened
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(in pressure per minute) and the tunnels you could use to move between
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the valves.
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There's even a valve in the room you and the elephants are currently
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standing in labeled =AA=. You estimate it will take you one minute to
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open a single valve and one minute to follow any tunnel from one valve
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to another. What is the most pressure you could release?
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For example, suppose you had the following scan output:
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#+begin_example
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Valve AA has flow rate=0; tunnels lead to valves DD, II, BB
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Valve BB has flow rate=13; tunnels lead to valves CC, AA
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Valve CC has flow rate=2; tunnels lead to valves DD, BB
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Valve DD has flow rate=20; tunnels lead to valves CC, AA, EE
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Valve EE has flow rate=3; tunnels lead to valves FF, DD
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Valve FF has flow rate=0; tunnels lead to valves EE, GG
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Valve GG has flow rate=0; tunnels lead to valves FF, HH
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Valve HH has flow rate=22; tunnel leads to valve GG
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Valve II has flow rate=0; tunnels lead to valves AA, JJ
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Valve JJ has flow rate=21; tunnel leads to valve II
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#+end_example
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All of the valves begin /closed/. You start at valve =AA=, but it must
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be damaged or jammed or something: its flow rate is =0=, so there's no
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point in opening it. However, you could spend one minute moving to valve
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=BB= and another minute opening it; doing so would release pressure
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during the remaining /28 minutes/ at a flow rate of =13=, a total
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eventual pressure release of =28 * 13 = 364=. Then, you could spend your
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third minute moving to valve =CC= and your fourth minute opening it,
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providing an additional /26 minutes/ of eventual pressure release at a
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flow rate of =2=, or =52= total pressure released by valve =CC=.
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Making your way through the tunnels like this, you could probably open
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many or all of the valves by the time 30 minutes have elapsed. However,
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you need to release as much pressure as possible, so you'll need to be
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methodical. Instead, consider this approach:
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#+begin_example
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== Minute 1 ==
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No valves are open.
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You move to valve DD.
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== Minute 2 ==
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No valves are open.
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You open valve DD.
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== Minute 3 ==
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Valve DD is open, releasing 20 pressure.
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You move to valve CC.
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== Minute 4 ==
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Valve DD is open, releasing 20 pressure.
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You move to valve BB.
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== Minute 5 ==
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Valve DD is open, releasing 20 pressure.
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You open valve BB.
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== Minute 6 ==
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Valves BB and DD are open, releasing 33 pressure.
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You move to valve AA.
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== Minute 7 ==
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Valves BB and DD are open, releasing 33 pressure.
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You move to valve II.
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== Minute 8 ==
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Valves BB and DD are open, releasing 33 pressure.
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You move to valve JJ.
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== Minute 9 ==
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Valves BB and DD are open, releasing 33 pressure.
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You open valve JJ.
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== Minute 10 ==
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Valves BB, DD, and JJ are open, releasing 54 pressure.
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You move to valve II.
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== Minute 11 ==
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Valves BB, DD, and JJ are open, releasing 54 pressure.
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You move to valve AA.
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== Minute 12 ==
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Valves BB, DD, and JJ are open, releasing 54 pressure.
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You move to valve DD.
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== Minute 13 ==
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Valves BB, DD, and JJ are open, releasing 54 pressure.
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You move to valve EE.
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== Minute 14 ==
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Valves BB, DD, and JJ are open, releasing 54 pressure.
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You move to valve FF.
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== Minute 15 ==
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Valves BB, DD, and JJ are open, releasing 54 pressure.
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You move to valve GG.
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== Minute 16 ==
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Valves BB, DD, and JJ are open, releasing 54 pressure.
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You move to valve HH.
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== Minute 17 ==
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Valves BB, DD, and JJ are open, releasing 54 pressure.
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You open valve HH.
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== Minute 18 ==
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Valves BB, DD, HH, and JJ are open, releasing 76 pressure.
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You move to valve GG.
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== Minute 19 ==
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Valves BB, DD, HH, and JJ are open, releasing 76 pressure.
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You move to valve FF.
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== Minute 20 ==
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Valves BB, DD, HH, and JJ are open, releasing 76 pressure.
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You move to valve EE.
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== Minute 21 ==
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Valves BB, DD, HH, and JJ are open, releasing 76 pressure.
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You open valve EE.
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== Minute 22 ==
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Valves BB, DD, EE, HH, and JJ are open, releasing 79 pressure.
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You move to valve DD.
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== Minute 23 ==
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Valves BB, DD, EE, HH, and JJ are open, releasing 79 pressure.
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You move to valve CC.
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== Minute 24 ==
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Valves BB, DD, EE, HH, and JJ are open, releasing 79 pressure.
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You open valve CC.
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== Minute 25 ==
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Valves BB, CC, DD, EE, HH, and JJ are open, releasing 81 pressure.
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== Minute 26 ==
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Valves BB, CC, DD, EE, HH, and JJ are open, releasing 81 pressure.
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== Minute 27 ==
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Valves BB, CC, DD, EE, HH, and JJ are open, releasing 81 pressure.
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== Minute 28 ==
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Valves BB, CC, DD, EE, HH, and JJ are open, releasing 81 pressure.
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== Minute 29 ==
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Valves BB, CC, DD, EE, HH, and JJ are open, releasing 81 pressure.
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== Minute 30 ==
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Valves BB, CC, DD, EE, HH, and JJ are open, releasing 81 pressure.
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#+end_example
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This approach lets you release the most pressure possible in 30 minutes
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with this valve layout, =1651=.
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Work out the steps to release the most pressure in 30 minutes. /What is
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the most pressure you can release?/
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Your puzzle answer was =1737=.
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** --- Part Two ---
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You're worried that even with an optimal approach, the pressure released
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won't be enough. What if you got one of the elephants to help you?
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It would take you 4 minutes to teach an elephant how to open the right
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valves in the right order, leaving you with only /26 minutes/ to
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actually execute your plan. Would having two of you working together be
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better, even if it means having less time? (Assume that you teach the
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elephant before opening any valves yourself, giving you both the same
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full 26 minutes.)
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In the example above, you could teach the elephant to help you as
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follows:
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#+begin_example
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== Minute 1 ==
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No valves are open.
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You move to valve II.
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The elephant moves to valve DD.
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== Minute 2 ==
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No valves are open.
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You move to valve JJ.
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The elephant opens valve DD.
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== Minute 3 ==
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Valve DD is open, releasing 20 pressure.
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You open valve JJ.
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The elephant moves to valve EE.
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== Minute 4 ==
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Valves DD and JJ are open, releasing 41 pressure.
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You move to valve II.
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The elephant moves to valve FF.
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== Minute 5 ==
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Valves DD and JJ are open, releasing 41 pressure.
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You move to valve AA.
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The elephant moves to valve GG.
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== Minute 6 ==
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Valves DD and JJ are open, releasing 41 pressure.
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You move to valve BB.
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The elephant moves to valve HH.
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== Minute 7 ==
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Valves DD and JJ are open, releasing 41 pressure.
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You open valve BB.
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The elephant opens valve HH.
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== Minute 8 ==
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Valves BB, DD, HH, and JJ are open, releasing 76 pressure.
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You move to valve CC.
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The elephant moves to valve GG.
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== Minute 9 ==
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Valves BB, DD, HH, and JJ are open, releasing 76 pressure.
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You open valve CC.
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The elephant moves to valve FF.
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== Minute 10 ==
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Valves BB, CC, DD, HH, and JJ are open, releasing 78 pressure.
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The elephant moves to valve EE.
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== Minute 11 ==
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Valves BB, CC, DD, HH, and JJ are open, releasing 78 pressure.
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The elephant opens valve EE.
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(At this point, all valves are open.)
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== Minute 12 ==
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Valves BB, CC, DD, EE, HH, and JJ are open, releasing 81 pressure.
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...
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== Minute 20 ==
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Valves BB, CC, DD, EE, HH, and JJ are open, releasing 81 pressure.
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...
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== Minute 26 ==
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Valves BB, CC, DD, EE, HH, and JJ are open, releasing 81 pressure.
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#+end_example
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With the elephant helping, after 26 minutes, the best you could do would
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release a total of =1707= pressure.
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/With you and an elephant working together for 26 minutes, what is the
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most pressure you could release?/
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Your puzzle answer was =2216=.
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Both parts of this puzzle are complete! They provide two gold stars: **
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