# The famous task of Edward Luke

At a scientific congress during breakfast, which was attended by many famous mathematicians from different countries, the French mathematician **Eduard Luca** announced to his assembled colleagues that he wants to offer them one of the most difficult tasks: suppose that every day at noon he leaves from Le Havre to New York a ship and at the same time a ship of the same company departs from New York to Le Havre. Moving both to that and to the other side takes exactly 7 days. How many ships of this company, going in opposite directions, will meet a ship leaving today at noon from Le Havre?

Some of those present, celebrities in the field of mathematics, tell about this case of Luke in their "Entertaining Mathematics", without thinking twice, exclaimed that seven. Most were silent. No one gave the correct answer. However, if we use the timetable of the ships shown in the figure, then the solution would appear with complete clarity, clearly and convincingly. Those present when solving the famous task of Luke took into account only those ships that were supposed to hit the road, forgetting about those that were already on the road.

The drawing clearly shows that the ship, the path of which the AB line depicts, will meet 13 ships at sea, and in addition, two more - one that arrived in Le Havre at the time of its departure, and one departing from New York at the time of its arrival there. Thus, in total he will meet 15 ships on his way. At the same time, the graph also shows that ships will meet daily at noon and midnight.

If someone began to doubt the usefulness of solving problems with the help of graphs, then the above solution to this famous task should resolve such a doubt. The difficult task of Edward Luke in such lighting becomes simple and completely obvious.