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IMSO 2004 Mathematics – International Exploration Question 5

IMSO Maths · IMSO 2004 Mathematics – International Exploration

Question 5

Popon is to deliver newspapers along the streets in his neighborhood. He is paid by the distance he makes, and thus the farther he makes, the higher the pay is. While he can cross any intersection as many times as he likes, he cannot pass any street more than once (a street is one segment between 2 adjacent points).

For example, in a neighborhood which looks like this, Popon is to start from K and to finish at O. To get the highest payment, he takes the longest possible route. One possibility is indicated by 1-2-3-4-5-6-7-8 in the figure below.

Question illustration

If the neighborhood looks like the following picture, what is the longest possible route from A to B? Trace and indicate the route by writing numbers 1, 2, 3, ... on the streets of the route.

Question illustration

Diagram labels: each horizontal street is 50 m; each vertical street is 30 m.