MathDB

A biologist watches a chameleon. The chameleon catches flies and rests after each catch. The biologist notices that: [*]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.
[*]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?

Problem Statement