Day 15.

15.py

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+#!/usr/bin/python3
+
+import itertools
+import re
+
+input_matcher = re.compile(r'^Disc #(.*?) has (.*?) positions; at time=0, it is at position (.*?)\.$')
+
+# Returns a generator for positions that this disc will be at when the capsule arrives. e.g. if disc 3 starts at
+# position 0 at time 0, the first returned position will be 3 (because the disc will have ticked around three times
+# before a capsule released at t=0 arrives).
+positions = lambda disc: ((disc[0] + disc[2] + i) % disc[1] for i in itertools.count())
+
+
+def run(lines):
+    # Pull the information out from the text line, making sure we treat numbers as ints.
+    discs = map(lambda line: tuple(map(int, input_matcher.match(line).groups())), map(str.strip, lines))
+
+    # Zip together the positions of each disc. That means the first element in combos will show the positions each
+    # disc will be at when the capsule arrives if it's released at t=0; the second element will be the positions for
+    # a capsule released at t=1, etc.
+    combos = zip(*map(positions, discs))
+
+    # Find a time when all discs will be at position 0 for the arrival of the capsule.
+    times = (i for i, c in enumerate(combos) if all(p == 0 for p in c))
+    return next(times)
+
+with open('15.txt', 'r') as file:
+    lines = file.readlines()
+    print("Step 1: %s" % run(lines))
+    print("Step 2: %s" % run(lines + ['Disc #7 has 11 positions; at time=0, it is at position 0.']))

15.txt

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+Disc #1 has 17 positions; at time=0, it is at position 5.
+Disc #2 has 19 positions; at time=0, it is at position 8.
+Disc #3 has 7 positions; at time=0, it is at position 1.
+Disc #4 has 13 positions; at time=0, it is at position 7.
+Disc #5 has 5 positions; at time=0, it is at position 1.
+Disc #6 has 3 positions; at time=0, it is at position 0.