This trick works for any number that ends in 5! Here's what you do...

Any number that ends in 5 has a square that ends in 25, so the last 2 digits of your square are going to be 25. To get the rest of it, you take the number you want to square, and chop off the last 5 (i.e. if you are doing 75, you take 7. If you are doing 1435, you take 143 etc.) You take your number without the 5, and times it by itself-plus-one (i.e. if you are doing 75, you have 7 x 8. If you are doing 1435, you have 143 x 144 etc.) Whatever that number is is the first digits of your square except the last two, which are your original 25.

E.g. The square of 65 is 4225 (6 x 7 = 42, 25)

Ooh the number of arguments I've had with people over this one (including my Year 10 maths teacher...)

Well, there are 2 "proofs" that I know of. The first proof is that:

0.111111... = one ninth
Then you times both sides by 9.

0.999999... = nine nineths
0.999999... = 1

The second proof is a little more complex.

Let 'k' equal 0.999999... (remember that 0.999999... never stops.)

k = 0.999999...
10k = 9.999999...
Therefore, 10k - k = 9.999999... - 0.999999...
9k = 9
k = 1
Therefore 0.999999... = 1

Interesting, isn't it? Go and have a think about it. Against all reason, it actually works.

This is the other side of the argument. It's perfectly valid!

Again two arguments. The first one:

1 - 0.9 = 0.1
1 - 0.99 = 0.01
1 - 0.999 = 0.001
1 - 0.999999... = 0.00000...1
Therefore 0.999999... is not equal to 1.

The second one:

If you have the graph of

y(x - 1) = 1 (which is a hyperbola)
you can see that there are two asymptotes (i.e. where the line approaches and gets infinitely close to but never ever touches):

y = 0, and x = 1.
If you try to substitute x = 1 into the equation:

y(1 - 1) = 0
0y = 1
which makes absolutely no sense, as there is no number which multiplies with zero to give you 1. Because x = 1 is an asymptote, the line gets infinitely close to it, but never touches it. In this case, it is possible to get a value of y if you substitute in x = 0.999999... , as you would get if you substituted any value of x which was not equal to 1. Therefore 0.999999... is not equal to 1.

It's a simple trick, but you'll find that most people you try it on either don't get it, or don't even see that you're doing it. If you want a detailed explanation of how it works, and this is only for people who understand probability thoroughly, go here. For those of you who only want the trick, read on.

Okay, this is how you set up the trick. You need 1 coin, and a pen and paper. What the idea is, is that each of you writes down a sequence of 3 tosses, (eg: THH or HTH), and you toss the coin, and keep tossing it until one of the 2 sequences happens in order, and whichever sequence happens first is the winner (eg: if you continually toss the coin so that it lands: T,H,T,T,T,H,T,H, the person who wrote HTH wins, because the last 3 tosses were a HTH, and a THH hasn't appeared yet.)

Now to set up the trick. First, you get the other person to write down their sequence of 3. Suppose they write down TTH. What you do for your sequence of 3 is, you cross off their last letter (so you've got TT), and add your own letter on the front, but make sure it doesn't read the same backwards as forwards (ie: don't have TTT, or HTH or anything like that.)In this case, you'd add a H, and have HTT. Suppose they write down HTT. Cross off the last letter (leaving it with HT), and add your other number on the front, making sure it's not the same forwards and backwards (ie: add a H, so you get HHT.)

I don't know how it works, but I'll show you some results I got, by tossing the coin myself - and this is actually real for those of you out there who don't believe me!

Other person's number	Times they won	My number	Times I won
THH	2/10	TTH	8/10
TTH	2/10	HTT	8/10
HHH	2/10	THH	8/10

I actually did them just then, as I was writing this section of the page, and I really am surprised!!! Geez! I never actually expected them to turn out that accurate, it was just something I saw on TV, and worked out the probability for, I never expected it to be THAT exact! If you're now interested in how it all works, see this page. Try it for yourself!