Three people check into a hotel. They pay £30 to the manager and go to their room. The manager suddenly remembers that the room rate is £25 and gives £5 to the bellboy to return to the people. On the way to the room the bellboy reasons that £5 would be difficult to share among three people so he pockets £2 and gives £1 to each person. Now each person paid £10 and got back £1. So they paid £9 each, totalling £27. The bellboy has £2, totalling £29. Where is the missing £1?
Hint: Be careful of what you're adding.
We have to be careful what we are adding together.
Originally, they paid £30, they each received back £1, they now have only paid £27. Of this £27, £25 went to the manager for the room and £2 went to the bellboy.
Would you believe that this amazing sentence contains ninety two letters, one comma and a single question mark?
Answer: This is not really a puzzle, merely a curious and clever piece of text.
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?
Hint: This puzzle needs some very careful thinking.
Since the arrow does indeed hit the target, it must be true that 1/2 + 1/4 + 1/8 + ... = 1.
This is because the sum of an infinite series can be a finite number.
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, so 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!
Hint: Be careful not to let your brain melt on this one.
Answer: This puzzle is a classic paradox. You are led through a sequence of seemingly valid arguments which lead to a conclusion, which quite clearly cannot be true.
Consider an arrow in flight towards a target.
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?
Hint: This is a puzzle to melt the brain!
Answer: The arrow clearly reaches the target.
This is a classic paradox, attributed to Zeno of Elea, a Greek philosopher from Italy. Great minds over the centuries have pondered this paradox, and the scope of a solution is beyond the space available here. It is not even clear that a solution to the paradox actually exists.