IMO Shortlist 1999 problem C3
Kvaliteta:
Avg: 0,0Težina:
Avg: 7,0 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
fly is the same as the resting period before catching the
fly and one minute shorter than the resting period before catching the
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
minutes in a row ?
- After how many minutes will the chameleon catch his
fly ?
- How many flies were caught by the chameleon after 1999 minutes have passed ?
- the first fly is caught after a resting period of one minute;
- the resting period before catching the
![2m^{th}](/media/m/7/2/7/7274424ef295288c27225a704c507d49.png)
![m^{th}](/media/m/9/2/2/9222c150af81684415046260007d008f.png)
![(2m+1)^{th}](/media/m/3/a/5/3a5dcae6c8d6924c4b036ae0298fca63.png)
- 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](/media/m/7/f/0/7f02ff2403dbf63ddc4395762441de88.png)
- After how many minutes will the chameleon catch his
![98^{th}](/media/m/b/8/1/b8104a72810607d79f7376a1c0945876.png)
- How many flies were caught by the chameleon after 1999 minutes have passed ?
Izvor: Međunarodna matematička olimpijada, shortlist 1999