ISL 1999 C3

A biologist watches a chameleon. The chameleon catches flies and rests after each catch. The biologist notices that: [list=1][]the first fly is caught after a resting period of one minute; []the resting period before catching the $2m^\text{th}$ fly is the same as the resting period before catching the $m^\text{th}$ fly and one minute shorter than the resting period before catching the $(2m+1)^\text{th}$ fly; [*]when the chameleon stops resting, he catches a fly instantly.[/list]

[list=a][]How many flies were caught by the chameleon before his first resting period of $9$ minutes in a row? []After how many minutes will the chameleon catch his $98^\text{th}$ fly? [*]How many flies were caught by the chameleon after 1999 minutes have passed?[/list]

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