A logic / mathematical diversion

[Mjolinor]

NO GOOGLING

You have 2 candles that will burn for 1 hour each.
These candles burn at an unpredictable rate, not unit length per unit time period. eg it may burn 3 inches in 2 minutes, next 2 inches in 10 minutes and the last inch in 48 minutes, you just do not know.

As it is a logic / maths puzzle you have to assume it takes zero time to light a candle or put one out and zero time to do anything else you may want to do with the candles (please do not enlighten us at to what other uses you have for candles).

How can you time 45 minutes.

I sort of thought it was obvious from the type of question but you do not have a watch or any other way of counting time passing.

[flyingpig]

Look at your watch, and when it is at 12:00:00 exactly, light the candles. When your watch says 12:45:00 you know they have been burning for 45 minutes exactly.

Next!!

FP.

[Evastar]

light one candle, and then light the other one fifteen minutes later. when the first candle goes out you know its 45 mins since you lit the second one

[Mjolinor]

light one candle, and then light the other one fifteen minutes later. when the first candle goes out you know its 45 mins since you lit the second one

And you know 15 minutes after you lit the first candle by some secret internal clock you had when you were born maybe or perhaps a bit of divine intervention?

[Shady]

can we break the candles?
if so, then the wick folded in half and half again would be 15 minutes long yeah?
so if you tape that folded wick to the other candle, then light the candle, when it burns down to the tip of the taped wick then 45 minutes have passed.
i hate you for making me waste half hour on this and its probably wrong

[Egren71]

I don't think that would work as it doesn't allow for the uneven burn of the candles.
This is how i think you would need to do it.
Cut 1 candle in half a light both pieces and light the uncut candle. Assuming they don't burn evenly of the two cut pieces one will burn out before the other.
At the point when one is burnt out and the other is still burning take the still burning one and cut that in half and relight both pieces. Repeat this until both pieces have burnt out.
At this point you know that it has been half an hour.
Now take the candle that you didn't cut which should be part used at this point and cut it in half and repeat the process.
At this point you know that another quarter of an hour has passed thereby giving you your 45 minutes.
Of course this is only accurate if you take no time to light, put out and cut candles.

[ChelseaBun]

This is doing my head in

cut one candle in half and then light all three pieces together.

Then when the two little pieces have burned that is half an hour past?

Then cut whats left of the big bit in half and burn those two together and that will take 15 minutes, equaling 45 minutes?

[ChelseaBun]

p.s please post some more

[Egren71]

I suppose an easier way to do it would be to light both ends of one candle and only one end of the other.
When the candle that has been lit on both ends goes out. Then light the other end of the one that you lit only on one end.
This would also give you your 45 minutes. Assuming that there was no strangeness to the burn time of the candles having them laying on their sides

[Shady]

i think mj should be banned for winding people up

[ChelseaBun]

you cant burn a candle on both ends? Whats holding the candle in the middle?
The wax would melt over the flames and put it out though?


yeh agreed shady, a 5 month ban for causing confusion

[Egren71]

Yes i don't think it would work in the real world, only as a maths problem.
As for whats holding it in the middle, i was thinking of laying it down on a brick or something that doesn't burn.
And although i have never tried it i would have thought that laying it down would make it burn faster as the wick wouldn't have to melt so much wax to expose more of the wick.

[flyingpig]

Thats it..Burn one candle at both ends when it goes out that is 30 minutes.

Split the other in 2 and burn one section at both ends that will expire after 15 minutes.

When candle one has extinguished light candle 2 then it has been 45 mins...

Back of the net!! Hey presto!! Voila! Easy Peasy Lemon Squeezy!!

[Mjolinor]

Yes i don't think it would work in the real world, only as a maths problem.
As for whats holding it in the middle, i was thinking of laying it down on a brick or something that doesn't burn.
And although i have never tried it i would have thought that laying it down would make it burn faster as the wick wouldn't have to melt so much wax to expose more of the wick.

But it's a theoretical exercise so physical constraints don't apply.

I will leave comments for later, maybe tomorrow so other people can play with it.

[Mjolinor]

Thats it..Burn one candle at both ends when it goes out that is 30 minutes.

Split the other in 2 and burn one section at both ends that will expire after 15 minutes.

When candle one has extinguished light candle 2 then it has been 45 mins...

Back of the net!! Hey presto!! Voila! Easy Peasy Lemon Squeezy!!

Try again