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?
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.
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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?
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.
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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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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?
This puzzle is a classic one that 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.
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