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+--- Day 20: Pulse Propagation ---
+
+Modules communicate using pulses. Each pulse is either a high pulse or a low pulse. When a module sends a pulse, it sends that type of pulse to each module in its list of destination modules.
+
+There are several different types of modules:
+
+Flip-flop modules (prefix %) are either on or off; they are initially off. If a flip-flop module receives a high pulse, it is ignored and nothing happens. However, if a flip-flop module receives a low pulse, it flips between on and off. If it was off, it turns on and sends a high pulse. If it was on, it turns off and sends a low pulse.
+
+Conjunction modules (prefix &) remember the type of the most recent pulse received from each of their connected input modules; they initially default to remembering a low pulse for each input. When a pulse is received, the conjunction module first updates its memory for that input. Then, if it remembers high pulses for all inputs, it sends a low pulse; otherwise, it sends a high pulse.
+
+There is a single broadcast module (named broadcaster). When it receives a pulse, it sends the same pulse to all of its destination modules.
+
+There is a module with a single button on it called the button module. When you push the button, a single low pulse is sent directly to the broadcaster module.
+
+After pushing the button, you must wait until all pulses have been delivered and fully handled before pushing it again. Never push the button if modules are still processing pulses.
+
+Pulses are always processed in the order they are sent. So, if a pulse is sent to modules a, b, and c, and then module a processes its pulse and sends more pulses, the pulses sent to modules b and c would have to be handled first.
+
+The module configuration (your puzzle input) lists each module. The name of the module is preceded by a symbol identifying its type, if any. The name is then followed by an arrow and a list of its destination modules. For example:
+
+broadcaster -> a, b, c
+%a -> b
+%b -> c
+%c -> inv
+&inv -> a
+
+In this module configuration, the broadcaster has three destination modules named a, b, and c. Each of these modules is a flip-flop module (as indicated by the % prefix). a outputs to b which outputs to c which outputs to another module named inv. inv is a conjunction module (as indicated by the & prefix) which, because it has only one input, acts like an inverter (it sends the opposite of the pulse type it receives); it outputs to a.
+
+By pushing the button once, the following pulses are sent:
+
+button -low-> broadcaster
+broadcaster -low-> a
+broadcaster -low-> b
+broadcaster -low-> c
+a -high-> b
+b -high-> c
+c -high-> inv
+inv -low-> a
+a -low-> b
+b -low-> c
+c -low-> inv
+inv -high-> a
+
+After this sequence, the flip-flop modules all end up off, so pushing the button again repeats the same sequence.
+
+Here's a more interesting example:
+
+broadcaster -> a
+%a -> inv, con
+&inv -> b
+%b -> con
+&con -> output
+
+This module configuration includes the broadcaster, two flip-flops (named a and b), a single-input conjunction module (inv), a multi-input conjunction module (con), and an untyped module named output (for testing purposes). The multi-input conjunction module con watches the two flip-flop modules and, if they're both on, sends a low pulse to the output module.
+
+Here's what happens if you push the button once:
+
+button -low-> broadcaster
+broadcaster -low-> a
+a -high-> inv
+a -high-> con
+inv -low-> b
+con -high-> output
+b -high-> con
+con -low-> output
+
+Both flip-flops turn on and a low pulse is sent to output! However, now that both flip-flops are on and con remembers a high pulse from each of its two inputs, pushing the button a second time does something different:
+
+button -low-> broadcaster
+broadcaster -low-> a
+a -low-> inv
+a -low-> con
+inv -high-> b
+con -high-> output
+
+Flip-flop a turns off! Now, con remembers a low pulse from module a, and so it sends only a high pulse to output.
+
+Push the button a third time:
+
+button -low-> broadcaster
+broadcaster -low-> a
+a -high-> inv
+a -high-> con
+inv -low-> b
+con -low-> output
+b -low-> con
+con -high-> output
+
+This time, flip-flop a turns on, then flip-flop b turns off. However, before b can turn off, the pulse sent to con is handled first, so it briefly remembers all high pulses for its inputs and sends a low pulse to output. After that, flip-flop b turns off, which causes con to update its state and send a high pulse to output.
+
+Finally, with a on and b off, push the button a fourth time:
+
+button -low-> broadcaster
+broadcaster -low-> a
+a -low-> inv
+a -low-> con
+inv -high-> b
+con -high-> output
+
+This completes the cycle: a turns off, causing con to remember only low pulses and restoring all modules to their original states.
+
+The answer is the number of low pulses multiplied by the number of high pulses when the button is pressed 1000 times.
+
+In the first example, the same thing happens every time the button is pushed: 8 low pulses and 4 high pulses are sent. So, after pushing the button 1000 times, 8000 low pulses and 4000 high pulses are sent. Multiplying these together gives 32000000.
+
+In the second example, after pushing the button 1000 times, 4250 low pulses and 2750 high pulses are sent. Multiplying these together gives 11687500.
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