[Guest]

1. You have been given an infinite number of ropes. All ropes are of varying length. If you burn any single rope such that it is lit from one end (and allowed to go on till it reaches the other end), the total time the rope takes to get burnt is one hour. Some parts burn faster than the others. Now a person comes along and claims that he can use this ‘burning ropes ’ method to exactly measure time of one hour and 15 mins (75mins). He doesn’t use any other method, source or tool (besides burning and observation) to measure time. How would you do it if put in the same situation? [Hint: You can burn ropes simultaneously]

2. You are given a stone, weighing 40 kg. Your job is to break it in four different parts such that they can then be used in a balance to accurately weigh all objects in the range from 1-40kg. What would be the individual weight of the four parts? (Assume that all objects to be measured have integer weights, i.e. no decimal numbers)

3. Using this image: http://i.imgur.com/3PPsW.png

Design a track through the lands so that you cross each of the seven connections labeled, only once. All connections have to be completely traversed exactly once. The track must be uni-directional, i.e. you cannot double-back and move the way you came. (This one seems impossible)

[curr3nt]

1, 3, 9 and 27

[Guest]

thnx but can u explain how u got them?

[curr3nt]

Anything with a minus goes on the other side of the balance.

1	   27-9-3-1	    27+1

3-1	 27-9-3		  27+3-1

3	   27-9-3+1	    27+3

3+1	 27-9-1		  27+3+1

9-3-1   27-9		    27+9-3-1

9-3	 27-9+1		  27+9-3

9-3+1   27-9+3-1	    27+9-3+1

9-1	 27-9+3		  27+9-1

9	   27-9+3+1	    27+9

9+1	 27-3-1		  27+9+1

9+3-1   27-3		    27+9+3-1

9+3	 27-3+1		  27+9+3

9+3+1   27-1		    27+9+3+1

	    27

[Guest]

1. Burn a rope from both ends: 30 minutes.

2. When that one is done, burn one rope from both ends (rope A), and another rope from one end (rope B).

3. When rope A is done (30 minutes), light the other end of rope B.

4. 75 minutes will have passed when rope B burns out.

[curr3nt]

Start burning three ropes at the same time.

#1 - Burn from one end

#2 - Burn from one end

#3 - Burn from both ends

#3 will burn out in 30 minutes. Once #3 is finished put out #2. #2 will have 30 minutes left.

Once #1 is finished start burning #2 from both ends for 15 minutes of burn.

[Guest]

The statement says that 'Some parts burn faster than the others.' Is your solution to question 1 still valid?

[Guest]

And the last 1 seems impossible to do, without adding another bridge? :S

[curr3nt]

The statement says that 'Some parts burn faster than the others.' Is your solution to question 1 still valid?

Burning from both ends will make it burn in half the time. The different parts burning at different rates only changes where it will meet, not length of the burn.

[Guest]

Thnx for the help any solution to the last 1?

[curr3nt]

I do not trust you enough to follow your link. Sorry.

[Guest]

The last one is impossible bacause there are 4 islands with an odd number of bridges. Puzzles like this can only be solved when 2 or less islands have an odd number of bridges. When 2 islands have an odd number of bridges, you can start at one and finnish at annother. When there are no islands with an odd number of bridges, you can start anywhere (even in the middle of a bridge!!!) and finnish in the same place.

[Guest]

No current, there's nothing to worry about. It is just a simple link trust me. why would i do something wrong?

Joekemon i have been thinking the exact same thing, on reading the question do u think tthat we are allowed to add a bridge? It says 'design' a track

[Guest]

I do not trust you enough to follow your link. Sorry.

Now you don't have to follow the link.

[Guest]

thnx^^

[Guest]

I found this http://en.wikipedia.org/wiki/Seven_Bridges_of_K%C3%B6nigsberg#Solutions

I think this might help

[Guest]

Does the above webpage suggest that this has no solution?

[Guest]

I thought the possible solution lay in the wording to the problem: "Design a track that allows you to cross the seven LABELED connections, only once." It does not deem additional connections are against the rules of the riddle. However, after reading your linked wikipedia, it seems that adding a bridge is definitely the only way to solve it. It's mathematically impossible unless you've added perimeters of your own accord. Also, you only need one more bridge, not the suggest three more in the link. Hope that helps.

[Guest]

the answer to the last please? there's no possible way of doing it without leaving out a bridge !!

[Guest]

Pretty easy

[Morningstar]

Design a track through the lands so that you cross each of the seven connections labeled, only once. All connections have to be completely traversed exactly once. The track must be uni-directional, i.e. you cannot double-back and move the way you came. (This one seems impossible)

Assuming the labeled connections are the only ones, adding another bridge is the only way to solve it. This was first posed by the mathematician Euler in regard to the bridges of the Russian city of Königsberg.

[Morningstar]

Whoops, just saw jaisha's Wikipedia link.