self Maths Puzzle

Shamu has to get home from his school to do some chores for his mother. The distance between the house and school is 3km if he walks along a straight line. Instead Shamu decides to go along two line segments to reach home such that, throughout his route , he is getting closer to home. What is the length (in km) of the longest route he can take? The figure below shows a valid and an invalid route that Shamu can take.

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self Other Question

A book contains 30 stories. Each story has a different number of pages under 31. The first story starts on page 1 and each story starts on a new page. What is the largest possible number of stories that can begin on odd page numbers? by 10 minutes past 5, the hour hand has turned through?