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--- pow:problem1f22 [2022/09/10 22:59] – created mazur
+++ pow:problem1f22 [2022/09/14 05:02] (current) – mazur
@@ Line 1: / Line 1: @@
+<box 85% round orange| Problem 1 (due on Monday, September 12)>
+Every day at noon a ship leaves Boston for London and another one leaves
+London for Boston. The travel takes exactly 7 days (168 hours) each way.
+John plans to travel to London next Sunday. How many ships coming from
+London will John see during his trip?
+</box>
+This was a warm-up puzzle. It is rather simple but has some nice history.
+The puzzle is attributed to a renowned French mathematician Edward Lucas.
+During a breakfast served for a scientific meeting with many world known
+mathematicians in attendance, Lucas announced this puzzle as
+one of the harder questions. According to Lucas' account, a few participants
+answered "7" without much thought, most remained silent, and nobody gave
+a correct answer. Of course, one should take anecdotes like this with a
+grain of salt.
+The answer to the puzzle is 15. The first ship John will see is the one which left London seven days before
+John starts his trip and enters Boston the moment John departs from it. The last ship John will see is the
+one which departs London the moment John arrives to it. John will see every ship "in-between" so it is easy
+to see that the number of ships John will see is 15. A graphical solution to this problem is {{:pow:2022f1.pdf|here}}.
+Some solvers were not sure if the two ships from London at the beginning and at the end of John's trip should
+be counted (which would make 13 the answer).
+One solver assumed that noon in London is 5 hours earlier than noon in Boston (which is correct, but it was not the intention of the problem to use the time difference). Under this assumption the answer is 14.