Math Is Fun Forum

ZHero

Real Member

Registered: 2008-06-08

Posts: 1,889

Butts & Cigarettes

Main puzzle is at the bottom....
Q: If 1 cigarette leaves 1 butt & 5 butts make a new cigarette then how many cigarettes can be made out of 121 butts?
A: 30! Its quite simple as 120 butts will make 24 cigarettes that would leave us with 24 butts which will combine with 1 butt left to make 5 more cigarettes which in turn will yield 1 more cigarette making a total of 30!

Now.. If the question be..

Find the LEAST no. of butts required to make 30 cigarettes if 1 cigarette leaves back 1 butt & 5 butts make 1 new cigarette?!
How to solve this??

"Zero is the real Hero, that's y i'm ZHero!"

Last edited by ZHero (2008-06-08 12:29:04)

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If two or more thoughts intersect, there has to be a point!

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Butts & Cigarettes

Make the 1st cigarette out of 5 butts.

After smoking it, you get 1 butt. Add 4 more butts to it to make the 2nd cigarette.

After smoking the second cigarette, add 4 more butts to make the 3rd cigarette.

So if a[sub]n[/sub] is the cumulative total number of butts required to make the nth cigarette,

Hence a[sub]30[/sub] = 121.
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ZHero

Real Member

Registered: 2008-06-08

Posts: 1,889

Re: Butts & Cigarettes

Make the 1st cigarette out of 5 butts.

After smoking it, you get 1 butt. Add 4 more butts to it to make the 2nd cigarette.

After smoking the second cigarette, add 4 more butts to make the 3rd cigarette.

So if a[sub]n[/sub] is the cumulative total number of butts required to make the nth cigarette,

Hence a[sub]30[/sub] = 121.
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Really Impressive!!
I'd been thinking over it for a few weeks but couldn't get it!!
More posts to come soon..
Love u.. Maths Forum!!

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If two or more thoughts intersect, there has to be a point!