Riddle time.

[clivehorridge]

I was about 14 when the school took us to a 'maths is fun' exhibition, a contradiction in terms for me, I hated maths!

It's the only one I remembered from that trip, but it was fascinating! Have you tried it algebraically?

It still works, you get 1089 from xyz or abc, whatever you choose. It was that that made me remember it.

 

[Chas]

I think this one may be a little tougher, go on prove me wrong.


Problem

You have two ropes coated in an oil to help them burn. Each rope will take exactly 1 hour to burn all the way through. However, the ropes do not burn at constant rates—there are spots where they burn a little faster and spots where they burn a little slower, but it always takes 1 hour to finish the job. And they don't burn at the same rate as each other because they are made of different materials.

With a lighter to ignite the ropes, how can you measure exactly 45 minutes?

 

[Shayne]

With a watch or clock .

 

[Chas]

With a watch or clock .

No, just the rope and lighter.

 

[Shayne]

if you laid the ropes out parallel to each other and then lit them at opposite ends would the flames meet at 45 minutes ?

 

[Chas]

if you laid the ropes out parallel to each other and then lit them at opposite ends would the flames meet at 45 minutes ?

No, they would meet at 30mins

 

[clivehorridge]

Place one end of one of the ropes to form a "T" then light only one of the open ends.

When both of the ropes have burned away, 45 minutes will have passed.

 

[Chas]

Place one end of one of the ropes to form a "T" then light only one of the open ends.

When both of the ropes have burned away, 45 minutes will have passed.

I don't think that would work Clive unless I've misunderstood you, as each rope takes an hour to burn away, whichever end you lit that rope would take 60 mins to burn, at the 30 min mark the second rope would start burning taking one hour so for both ropes to burn away would take two hours,
(each rope will burn for one hour)

 

[Shayne]

If you light one rope in middle it will burn towards both ends in half hour . Light the other rope in 3 places of equal distance and it will burn in 15 minutes ?

 

[chadr]

Line the ropes up in parallel but with only 1/2 of each overlapping. Light the ends and when the flames from the two meet in the overlapped section that should be 45mins?

If not, then I have no idea - my brain hurts!

 

[StarCruiser]

Fold each rope at their 3/4 lentghs so that the shorter end touches the longer length at the half way mark. Light the longer end and when the flame reaches the half way mark it will ignite the short end. When both ropes have burned away 45 minutes will have passed.

 

[Chas]

Line the ropes up in parallel but with only 1/2 of each overlapping. Light the ends and when the flames from the two meet in the overlapped section that should be 45mins?

If not, then I have no idea - my brain hurts!

Fold each rope at their 3/4 lentghs so that the shorter end touches the longer length at the half way mark. Light the longer end and when the flame reaches the half way mark it will ignite the short end. When both ropes have burned away 45 minutes will have passed.

Rich & Chadr, that wouldn't necessarily work as the rope burns at an erratic pace, the only given is that the total length will burn in one hour
To save you all buying some more Paracetamol here is the solution. I must admit I don't think I could have worked it out either.


Solution

Because the ropes burn at inconsistent rates, you can't simply measure 75 percent of the way down one rope and call that 45 minutes. The rope might burn slightly faster or slower in that last 25 percent. However, if you light one of the ropes on fire at both ends at the same time, it will burn up in 30 minutes, even if one side burns faster than the other.

So here's what you do: Light one of the ropes on fire on both ends and light the second rope on one end at the same time. When the first rope burns out, 30 minutes have elapsed. At that moment, you light the unlit end of the second rope.

Because 30 minutes of the second rope have already been used up, 30 more remain (though this does not necessarily mean that half of the rope's length has been burned, it could be more or less). Lighting the other end at the moment the first rope burns up will cause the remaining part of the second rope to burn up in 15 minutes. Once the second rope has been consumed by the flames, exactly 45 minutes have passed.

 

[clivehorridge]

We were all on right lines (I think) but not quite cracking it.

I totally forgot about each rope burning for an hour, so instead of 45 mins representing 3/4 of a rope, I got the fraction the other way up, as 1 1/2 ropes instead

Right lines, but wrong application. My life story it seems

 

[Chas]

We were all on right lines (I think) but not quite cracking it.

I totally forgot about each rope burning for an hour, so instead of 45 mins representing 3/4 of a rope, I got the fraction the other way up, as 1 1/2 ropes instead

Right lines, but wrong application. My life story it seems

I thought some of the answers were along the right lines and very close, well done guys. I'll look for another one.

 

[StarCruiser]

I'm off to sulk as I think mine was workable. I'm not bitter at all…

 

[Chas]

I'm off to sulk as I think mine was workable. I'm not bitter at all…

Yours would definitely have worked Rich but it didn't comply with the answer I had from my source, sorry no cigar.

 

[StarCruiser]

Still sulking…

 

[chadr]

Thinking about it (yes, I'm sad like that!), any solution that involves measuring/folding the ropes to get a fraction of the length i.e. like mine or SC's will be wrong as it implicitly assumes uniform burn rates - which I suppose is the whole point that you're told that it is not uniform in the first place!

 

[Chas]

A slightly different sort of riddle.
How many matchstick here?

 

[chadr]

8?