PUZZLE: THE FENCE PROBLEM

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?

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Time Management: Pomodoro Technique

Are you facing challenges in managing your time properly? If you often waste time on unproductive tasks and finally at the end of the day feel you have wasted your day. Pomodoro Technique may be a good solution to all your problems. Today I am going to discuss here, a very useful technique to improve your productivity and better time management. The credit for this technique goes to Francesco Cirillo. He utilized a tomato-shaped sandglass to manage his time effectively. He called it the Pomodoro technique (which is an Italian word for “tomato”). The idea behind the Pomodoro Technique is to break down all of your tasks into 25-minute time blocks. Between two session , keep a five-minute break. And after completing four Pomodoros sessions taking an extended break usually 15-20 min. There are six steps in the original technique: Decide on the task to be done. Set the Pomodoro timer (traditio...

Puzzle- 100 Prisoners and a Light Bulb

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...

Binding Rope Around The Earth

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...

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