Riddles..

1).You have to get from point A to point B. You don’t know if you can get there. What would you do?

2).Imagine you have a closet full of shirts. It’s very hard to find a shirt. So what can you do to organize your shirts for easy retrieval?

3).What method would you use to look up a word in a dictionary?

4).You have eight balls all of the same size. 7 of them weigh the same, and one of them weighs slightly more. How can you fine the ball that is heavier by using a balance and only two weighings?

5).How do you cut a rectangular cake into two equal pieces when someone has already taken a rectangular piece from it? The removed piece an be any size or at any place in the cake. You are only allowed one straight cut.

Burning Fuses

Two Fuses

You are given two fuses and a lighter. The fuses take one hour to burn. They burn at non-constant unknown rates; meaning it could take 40 minutes to burn half way and then 20 minutes for the other half, you do not know. You are told to make a timer using these fuses that will burn for 45 minutes. You can cut them, tie them in a bow, use them to floss with. . . anything you want.


Solution below..

Light both ends of one fuse and one end of the second. When the one you lit at both ends burns out, light the other end of the second one. When the second fuse burns out 45 minutes will have gone by.



This is because it takes half an hour for a fuse to burn completely through when lit from both ends and 15 minutes for the other half of the second fuse to burn through lit at both ends. You must convince yourself of this fact. Imagine a candle stick, if lit from both ends it would burn out in half the time.



Proof that it takes half the time of a fuse cut in half when the fuse is lit at both ends for non-constant fuses:



Consider our fuse being as long as a meter stick(arbitrary length, I could have picked any length as long as it takes one hour to burn when lit at one end)

Assume it takes an hour to burn when lit from one end.

Now lets say that after 30 minutes the fuse burned to the 30 cm (arbitrary mark) mark when lit from the 0 cm mark. What I have to now show is that it takes 30 minutes for the fuse to burn from the 100 cm mark to 30 cm.

If it did not take 30 minutes for the fuse to burn from the 100 cm mark to the 30 cm mark, the total burn time of the rope would not equal one hour.



For the second fuse, the key is that after the first fuse burns, whatever point the second fuse is at is the half burn time point for the second. Lighting the other end of the second fuse at this time will cause the 30 minutes of burn time the second fuse has left to become 15 minutes.