First things first .... what even is a paradox? Well, a paradox is a statement which at first sounds a bit like nonsense but when it is given some proper thought begins to make some sense. A very simple example would be the saying 'You have to spend money to save money'. How can that be right?!? If I'm spending it I'm definitely not saving it! .... but if I buy an energy efficient light-bulb to replace an ordinary light-bulb then I am immediately saving money and eventually I will have saved more than the cost of the new bulb. So in that case it was true that spending money also saved me money.
So here's the brain teaser. Zeno said that it is impossible to ever arrive at the place you want to get to!
He says you'll set off but you'll never arrive.
Now that's definitely a paradox! We all know that everyday - without fail - we move from one place to another ..... we walk to the kitchen .... or we drive to school .... or we fly to another country .... so how can Zeno suggest that we will never arrive anywhere?!?
To try and explain his logic we'll use the example of somebody called Gru (pronounced 'Groo' if you didn't already know) walking from one side of a room (which we'll call Point A) to a door on the other side of the room (which we'll call a door).
For Gru to walk between Point A and the door he will have to pass the half-way mark.
Nobody can argue with that! Let's call the half-way mark Point B
So Gru reaches Point B in the centre of the room ..... and he now needs to walk between Point B and the door.
For Gru to walk from Point B to the door he will have to pass the half-way mark between those two points.
Sounds reasonable enough so far doesn't it?. Let's call the half-way mark between Point B and the door Point C.
So Gru reaches Point C ..... and he now needs to walk between Point C and the door.
For Gru to walk from Point C to the door he will have to pass the half-way mark between those two points. Let's call that Point D
So he reaches Point D.... and he now needs to walk between Point D and the door.
For Gru to walk from Point D to the door he will have to pass the half-way mark between those two points. Let's call that Point E.
Are you beginning to see why this is a brain teaser?
Logically, that pattern will continue forever. Whenever you want to get anywhere you must first reach the half-way point .... which generates another half-way point .... which generates another half-way point ... over and over again. This is why Zeno's Paradox says that we can never arrive at the place we're trying to get to.
Well we did warn you that this particular brain teaser is most suitable for older children and teenagers! It may help if you grab a pencil and some paper and work it through visually (whilst this won't solve the paradox it may help you understand the puzzle a little better!). It depends on how your brain is wired as to how clear or complicated this conundrum is. Mathematically we can think of Point B as being 0.5 of the way across the room .... Point C as 0.25 of the way across the room .... Point D as being 0.125 of the way ... etc etc .... and this is an interesting way to start to understand why Zeno's Paradox appears to be logical ... and why ordinary maths won't solve the puzzle.