Fun Math Puzzles to LEARN From Part 2

The Cigarette Puzzle

Mr. Del Santo, my geometry teacher in high school, would present us with riddles and puzzles. This one is my favorites from the good ol’ days:

A homeless man can roll one full cigarette if he uses 10 cigarette butts. How many cigarettes can he possibly make if he collects 5,500 cigarette butts.

Well 5500÷10=550

“He can make 550 cigarettes!”

“…eh, not quite”

He has 550 cigarettes now… after he smokes those… then he’ll have 550 cigarette butts that he can use those to make even more cigarettes.


Now he has 55 more cigarette butts.

55÷10=5 with five remaining butts

When he smokes THOSE five he can use the remainder from before and the new butts to make one last cigarette

He can make 550+55+5+1=611 cigarettes with 5,500 cigarette butts.

This puzzle was important to me because I remember feeling tricked in class when I was asked to think about it. But I was so thrown off guard when my teacher told me I got it wrong because it was so simple. All I had to do was divide. It really made me realize that I look at problems without actually thinking about the point. What’s the point of this problem? If you’re homeless, and you can make use of these cigarette butts, you sure ain’t gonna waste a single one. You will take every possible opportunity that you can to make the most out of nothing. This problem teaches you to think outside the box and make the most out of nothing.


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