#
The imaginary Sea of Le has many (more than four) islands, and travel between them may only take place on bridges. Each pair of islands is connected by exactly one bridge, and no two bridges have the same length. The bridges cross over and under each other in a complex configuration, so the lengths of the bridges are unrelated to the direct distance between the islands which they connect.

Adi, Bai and Casey are each planning tours that visit each island exactly once, though the three of them do not necessarily start on the same island, and none of them return to their own starting island.

• Casey carefully plans the journey before starting out, finding the best starting island and a route that visits each island along a route that minimizes the sum total of the lengths of the bridges traveled.

• Adi, though, starts on a random island and plans a journey one island at a time. At each island along the way, Adi selects the shortest bridge from that island to an island not yet visited.

• Bai, who prefers a scenic route, also starts on a random island and, at each island along the way, Bai selects the longest bridge from that island to an island not yet visited.

For all three questions below, either show that the proposal is possible by constructing an example or prove why it is not possible.

a. Is it possible that the total length of Casey's journey over bridges is strictly less than Adi's?

b. Is it possible that all three journeys (Adi's, Bai's, and Casey's) have the same total length?

c. Is it possible that the total length of Bai's journey is strictly less than Adi's?

Attachments:

## Answers

Answered by

0

**Answer:**

where is this problem taken from? What contest?

**Step-by-step explanation:**

Similar questions

Physics,
5 days ago

Math,
5 days ago

Math,
11 days ago

Social Sciences,
11 days ago

Math,
7 months ago