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?
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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.
Think of words ending in -GRY. Angry and hungry are two of them. There are only three words in the English language. What is the third word? The word is something that everyone uses every day. If you have listened carefully, I have already told you what it is.
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Hint: Is this a trick question?
Answer: There are only two: angry and hungry. The rec.puzzles archive offers a large collection of words that end in -GRY, but none of them could be considered even remotely common. There are many generally unsatisfying "trick" answers to the problem, which depend on a specific wording of the question or that the question be spoken instead of written. There seems to be no agreement among puzzle historians about which form is the original, or even the age of the problem. In any event, it is apparent that the frequent mutations of the puzzle statement over the years have erased whatever answer was intended by the original author. The usual trick is to play on the expression "the English Language", you are then asked for the third word - which is of course Language!
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 porter to return to the people.
On the way to the room the porter reasons that £5 would be difficult to share among three people so they keep £2 and give £1 to each person.
Now each person paid £10 and got back £1.
So they paid £9 each, totalling £27. The porter has £2, totalling £29.
Where is the missing £1?
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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 porter.
There are three houses, and three utilities: water, gas and electricity.
Your task is to connect each house to all three utilities.
Therefore each house will have three lines and each utility will also have three lines.
However, you cannot cross lines! You cannot pass lines through houses or utilities. You cannot share lines.
Can you draw the 9 lines required?
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Hint: Try starting with the water.
This puzzle is a classic one which has no solution in 2D.
However, if you place the items on a doughnut shape in 3D you can solve it.
In the picture below, the electricity is linked to House 3 by going over the top and re-entering through the hole in the middle.