# Pick a Number

In this animation, the computer simulates a number of people $N$ choosing a number at random between 1 and $(\frac{N}{2})^2$. So, for example, it will simulate 400 people choosing a number between 1 and 40000.
How often would you expect it to pick the same number twice?

If you had Flash Player you would see that 400 people could choose a number between 1 and 40000, and there would be a duplicate around 80% of the time. Very surprising! You need to install the Adobe Flash Player to see the animation.

Click to enlarge the animation

Try it and see if it matches your guess. Click on the link below to see the animation in full screen.

In What are the chances? we show that the chance of there being no match is 13% when 20 people pick numbers between 1 and 100.

In Maths of coincidence we give a general formula that shows that the chance of there being no match is 13% whenever $(N/2)^2$ pick numbers at random between $1$ and $N$, whatever the choice of $N$.

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