Cigarette Butts

5

He makes 4 cigarettes with the 16 butts.

Then, he smokes them and has 4 more butts to make another cigarette.

I wrote up a quick simulation for this scenario:

Python 2.7:

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11

# pick up butts
butts = 16
cigarettes = 0
while butts >= 4:
    # make a cigarette
    butts -= 4
    cigarettes += 1
    # smoke it
    butts += 1
print "Answer:", cigarettes
print "Leftover butts:", butts

Michael can make $\boxed{5}$ cigarettes, with 1 butt left over.

Michael should also explore the possibility of $\boxed{better\ hygiene}$ .

He can make 4 cigarette buts from 16 cigarette buts.From 1 cigarette from 4 cigarette buts .Therefore the n.o. of cigarettes he can make from 16 cigarettes is 4+1=5