IITPAL

  Rope around The Earth: Wrap a thread tightly around the earth (along the equator). Now add an extra 2 meters of thread to this length and then wrap the new thread again around the earth in the same circular path (i.e. along the equator).                                                             (Image: Binding rope around the Earth) Now, how high do you think will the thread rise above from the ground ?(Or in other words, what will be the new radius corresponding to this new circumference?) Well, practically one might think that an addition of 2 meter won't make any difference since its too small compared to the size of the earth (which is ~6371000 meters in radius!). And even if it does, the difference will be so small (may be in millimeters or so) that it can easily be neglected? Well, le...

  A man wishes to fence in a perfectly square field which is to contain just as many acres as there are rails in the required fence. Each hurdle, or portion of the fence, is seven rails high, and two lengths would extend one pole (16½ ft.): that is to say, there are fourteen rails to the pole, lineal measure. Now, what must be the size of the field?

  Every once in a while, I hear puzzles about 100 prisoners and a meticulous, demanding warden. All of these puzzles share a common characteristic, a set of prisoners must work together to devise a clever scheme to thwart the warden. I hear these puzzles often enough that each time they reappear, I view them with an increased level of understanding corresponding to the stage of my mathematics education. Any problem may have a solution, but, sometimes, that solution may not be the most efficient one possible. For example, suppose you want to find something in your room but don’t remember where you put it. You can either search the room by yourself. Or you can call your (many) friends to help you. From a correctness standpoint, both solutions are correct. You’ll find what you’re looking for eventually. But from an algorithmic standpoint, the second solution where you search in parallel with your friends is better because it has a shorter runtime. The same holds for solutions to the 1...