Question 23
C3 (GBR). A biologist watches a chameleon. The chameleon catches flies and rests after each catch. The biologist notices that:
(i) the first fly is caught after a resting period of one minute;
(ii) the resting period before catching the $2m$th fly is the same as the resting period before catching the $m$th fly and one minute shorter than the resting period before catching the $(2m+1)$th fly;
(iii) when the chameleon stops resting, he catches a fly instantly.
(a) How many flies were caught by the chameleon before his first resting period of $9$ minutes?
(b) After how many minutes will the chameleon catch his $98$th fly?
(c) How many flies were caught by the chameleon after $1999$ minutes passed?
(i) the first fly is caught after a resting period of one minute;
(ii) the resting period before catching the $2m$th fly is the same as the resting period before catching the $m$th fly and one minute shorter than the resting period before catching the $(2m+1)$th fly;
(iii) when the chameleon stops resting, he catches a fly instantly.
(a) How many flies were caught by the chameleon before his first resting period of $9$ minutes?
(b) After how many minutes will the chameleon catch his $98$th fly?
(c) How many flies were caught by the chameleon after $1999$ minutes passed?