Brain Teasers

raj87verma88

I will most some mighty cool brain teasers here.

raj87verma88

Consider an arrow in flight. At any given moment of time, a snapshot could be taken of this arrow. In this snapshot, the arrow would not be moving. Let us now take another snapshot, leaving a very small gap of time between them. Again, the arrow is stationary. We can keep taking snapshots for each moment of time, each of which shows the arrow to be stationary. Therefore the overall effect is that the arrow never moves, however it still hits the target!
Where lies the flaw in the logic?

raj87verma88

You can imagine an arrow in flight, toward a target. For the arrow to reach the target, the arrow must first travel half of the overall distance from the starting point to the target. Next, the arrow must travel half of the remaining distance.

For example, if the starting distance was 10m, the arrow first travels 5m, then 2.5m.

If you extend this concept further, you can imagine the resulting distances getting smaller and smaller. Will the arrow ever reach the target?

raj87verma88

Would you believe that this amazing sentence contains ninety two letters, one comma and a single question mark?

raj87verma88

Assume that penguins live with a density of 1,000 penguins per square mile and can run at an average speed of 7 miles per hour on land and swim at 20 miles per hour. Also assume that a polar bear has a territory of 10 square miles, can run at 25 miles per hour and swim at 10 miles per hour, how many penguins will an average polar bear eat in any given month, remembering that a polar bear could, as a maximum, only eat one penguin per hour and 7% of the land is next to the sea.

The_Big_K

Quote:

Originally Posted by raj87verma88

Consider an arrow in flight. At any given moment of time, a snapshot could be taken of this arrow. In this snapshot, the arrow would not be moving. Let us now take another snapshot, leaving a very small gap of time between them. Again, the arrow is stationary. We can keep taking snapshots for each moment of time, each of which shows the arrow to be stationary. Therefore the overall effect is that the arrow never moves, however it still hits the target!
Where lies the flaw in the logic?

I don't see any flaw in the logic. Its pretty obvious. You're taking snapshots in which the distance between the target and the arrow is constantly decreasing. After some time, it will hit the target.

suyash

Quote:

Originally Posted by raj87verma88

You can imagine an arrow in flight, toward a target. For the arrow to reach the target, the arrow must first travel half of the overall distance from the starting point to the target. Next, the arrow must travel half of the remaining distance.

For example, if the starting distance was 10m, the arrow first travels 5m, then 2.5m.

If you extend this concept further, you can imagine the resulting distances getting smaller and smaller. Will the arrow ever reach the target?

the arrow wont reach the target ever...

since the addition of distance covered is a the sum of terms in geometric progression which is "tending to 10 mts"

raj87verma88

The answer lies in the theory of infinite series. I will give all the answers in one or two days. Till then let me see how many come up with the correct answers for all the problems.

The_Big_K

Quote:

Originally Posted by suyash

the arrow wont reach the target ever...

since the addition of distance covered is a the sum of terms in geometric progression which is "tending to 10 mts"

Why not? The arrow does travel 'half distances' always, as mentioned in the post.

Its like while typing this post, I typed the half of the post, then then half of remaining, then half of remaining - like that.

gohm

Well a photograph only shows objects as stationary. However the viewer would know the object is really moving. As long as the trajectory is correct and velocity, it will reach the target. Is this like if a tree falls in the woods and nobody is there to hear it, does it make a sound?

672 penguins at least. However we need to know which month to know number of days (672 is based on leap year month) and also how many polar bears as realistically you would not have only one polar bear (it would die out) and also polar bears sleep, eat other animals etc. which would reduce the number. The polar bear would hunt only on land and wait for the penguins which would have to return. OK so I know this isn't supposed to be a realistic problem... laugh.