## March 7, 2008

### Fuse Problem

You have two lengths of fuse. Each will burn for exactly one
hour. But the fuses are not necessarily identical and do
not burn at a constant rate. There are fast-burning sections
and slow-burning sections. How do you measure forty-five
minutes using only the fuses and a lighter?

hirender said...

if we can make better use of lighter it is possible to get the lengths

Anonymous said...

how?

Anonymous said...

how?

Anonymous said...

Burn the first piece at both ends - that will take 30min to be completely consumed. As soon as that finishes burn the 2nd at both ends and from the middle - that will then take another 15min.

Secret SquÃ¯rrel

vp said...

The problem with the above solution is that you dont knw where the middle of the candle is exactly.

Burn the first candle at both the ends. The first candle will burn out in 30 mins. Burn one end of the 2nd candle at the same time that you burn the 2 ends of the first candle. When the first candle burns out there will still be 30 mins left on the 2nd candle. At this point, burn the other end of the 2dnd candle. The 2nd candle will now burn out in 15 mins.

We have thus measured 45 mins

Anonymous said...

That's great but where did you get the candles from?

Obviously you just copied this answer from a differently-worded problem.

Neeraj said...

lioght both ends of one and only one end of the other fuse.
As soon as one with both ends lighted has burnt completely, light the other end of the other fuse so total time for burning both will be 30 + 15=45 mins

Anonymous said...

If there are fast-burning sections
and slow-burning sections how could you possibly know that each fuse would burn for one hour???

Anonymous said...

Burn fuse A at both ends, and same time burn fuse B at only one end.

fuse A will burn in 30 mins completely, while fuse B will always have been burning for 30 mins, but not completely.

We should have about 30 mins of fuse B now (provided it is burning from one end only)
We burn the other end for fuse B, so that it completes burning in 15 minutes completely.

so 30 minutes of fuse A + 15 mins of fuse B (after it has burnt for first 30 mins along with fuse A)