Puzzles 4U...Paradoxes

Puzzles 4U...

Paradoxes

Q01

Imagine an arrow in flight, toward a target. In order 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 we were to extend this concept further, we can imagine the resulting distances getting smaller and smaller. Will the arrow ever reach the target? Answer

Q02

Imagine a prisoner in a prison. He is sentenced to death and has been told that he will be killed on one day of the following week. He has been assured that the day will be a surprise to him, so he will not be anticipating the hangman on a particular day, thus keeping his stress levels in check.
The prisoner starts to think to himself, if I am still alive on Thursday, then clearly I shall be hanged on Friday, this would mean that I then know the day of my death, therefore I cannot be hanged on Friday. Now then, if I am still alive on Wednesday, then clearly I shall be hanged on Thursday, since I have already ruled out Friday. The prisoner works back with this logic, finally concluding that he cannot after all be hanged, without already knowing which day it was.
Casually, resting on his laurels, sitting in his prison cell on Tuesday, the warden arrives to take him to be hanged, the prisoner was obviously surprised! Answer

Q03

Again 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 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! Answer

Answers

A01
There is no answer to this question. Back

A02
There is no answer to this question. Back

A03
There is no answer to this question. Back

This page was last modifed on 20 September 1997.

	Puzzles 4U...

	Paradoxes
	Q01 Imagine an arrow in flight, toward a target. In order 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 we were to extend this concept further, we can imagine the resulting distances getting smaller and smaller. Will the arrow ever reach the target? Answer
	Q02 Imagine a prisoner in a prison. He is sentenced to death and has been told that he will be killed on one day of the following week. He has been assured that the day will be a surprise to him, so he will not be anticipating the hangman on a particular day, thus keeping his stress levels in check. The prisoner starts to think to himself, if I am still alive on Thursday, then clearly I shall be hanged on Friday, this would mean that I then know the day of my death, therefore I cannot be hanged on Friday. Now then, if I am still alive on Wednesday, then clearly I shall be hanged on Thursday, since I have already ruled out Friday. The prisoner works back with this logic, finally concluding that he cannot after all be hanged, without already knowing which day it was. Casually, resting on his laurels, sitting in his prison cell on Tuesday, the warden arrives to take him to be hanged, the prisoner was obviously surprised! Answer
	Q03 Again 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 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! Answer

	Answers
	A01 There is no answer to this question. Back
	A02 There is no answer to this question. Back
	A03 There is no answer to this question. Back


	This page was last modifed on 20 September 1997.