Escape Safely to The Ground!

You find yourself trapped at top an 800 foot tall building. The surrounding land is completely flat, plus there are no other structures nearby. You need to get to the bottom, uninjured, and can only safely fall about 5feet.

You look down the four walls; they are all completely smooth and featureless, except that one of the walls has a small ledge 400feet above the ground. Furthermore, there are two hooks, one on this ledge, and one directly above it on the edge of the roof. The only tools you have are 600feet of rope, and a knife.

 How do you get to the bottom? 

This should be your strategy! 

Strategy To Land Safely On The Ground

Why strategy needed to be planned?

1.Tie one end of the rope to the to hook and climb down to the ledge.

2. Cut (without dropping) the rope that hangs below the ledge, then climb back to the roof carrying the extra rope that you cut. You now have two lengths of rope: one that is 400 feet long and one that is 200 feet long.

3.At the top, untie the rope from the hook.

 Now setup the ropes like : Tie a small loop at one end of the 200-foot long rope. String the 400-foot long rope through the loop so that half of its length is on either side of the loop. Make sure that the loop is snug enough that the 400-foot long rope won't fall out by itself, but loose enough that you can pull the rope out later.

4. Now, tie the end of the 200-foot rope without the loop to the first hook. The 200-foot long rope lets you climb halfway to the ledge. 

5.For the remaining 200 feet, you carefully climb down the 400-foot rope, which hangs down 200 feet from where it is held by the loop. 

6.Once you get to the ledge, pull the 400-foot rope out of the loop.

7. Finally, tie it to the second hook, and climb the rest of the way to the ground.

A Determined Cat on a Ladder!

A ladder is leaning against a wall. On the center rung is a cat. She must be a very determined cat, because she remains on that rung as we draw the foot of the ladder away from the tree until the ladder is lying flat on the ground. What path does the cat describe as she undergoes this indignity?

She follows this path!

A Path Followed by Determined Cat

What was the question?

 Interestingly, the cat follows the circular path whose center is at the foot of tree. 

Actually, as ladder is drawn out a series of right triangles with the same hypotenuse (the ladder) are created with respect to the foot of tree.

The point of hypotenuses where cat is sitting determinedly will be always at the same distance from all 3 vertices. So if all such point are joined then we get a circular path having center at the foot of tree. 

(Figure is for illustration purpose only & may not have accurate measurements.

Maximum Runs That Batsman Can Score?

In a one day international cricket match, considering no extras(no wides, no ‘no’ balls, etc.) and no overthrows.

What is the maximum number of runs that a batsman can score in an ideal case ?

Note: Here we assume ideal and little practical scenario. We assume that batsman can not run for more than 3 runs in a ball, as otherwise there is no limit, he can run infinite runs(theoretically) in a ball, as far as opposite team does not catch the ball.”

Could be tricky! Here is correct number! 

Calculation of Maximum Runs by Batsman

What was the question?

It's not as straight forward as it seems at first glance. That is one might think that the maximum score that one can score by hitting 6 on every ball of 50 overs is 50 x 6 x 6 = 1800. 

No doubt, 1800 can be the maximum team score but not the individual score.Since batsman rotates strike every over, here both batsmen share these 1800 runs as 900 to each.

However, if the batsman on strike runs 3 runs on the last ball of the over then he can hit 5 more sixes in next over as strike is rotated back to him in next over. He can continue in this way till 49th over. And in 50th over he can hit 6 sixes on 6 balls.

Maximum Individual Score = 49 x [(5x6)+3]  + 36 = 1617 + 36 = 1653.

In this case, the batman at the non-striker end scores 0 runs as he doesn't get strike on a single ball.