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How do you calculate so quickly in your head?

One of the most frequently asked questions of me is “How do you calculate so quickly in your head?”
This question always reminds me of an old legend about a mathematician who lived a few centuries ago. He had a very rare talent. If he looked at a large quantity of anything (for example, the number of jellybeans in a big jar) he immediately could determine the exact number.
One day he was traveling in a horse carriage when another passenger pointed out a herd of sheep outside the window. Everybody peeked out the window to see the sheep. The mathematician did too and immediately said, “There are 1,452 sheep in the herd.”
Everybody exclaimed in surprise, “Excuse me, but how could you so quickly determine the number of sheep?”
The hero of our story replied: “It is very simple! I looked at the herd and immediately counted the number of sheep legs, then divided this number by four, and this way I got the answer!”
 
Now, on a serious note, on the one hand, I could describe here how I calculate in my head or to provide you with links to other websites where you can read about it, but, on the other hand, I wouldn't want to do it. And here is why. There are two schools of thought on how to solve different problems, tasks and so on. One way is to read everything you can find on the topic you try to discover, but on another hand, you shouldn't read anything about the topic, but try to solve the problem by yourself. First of all, this way you will be able to avoid mistakes that you can encounter in the literature and secondly if you are successful, you will get a lot of pleasure from solving the task yourself... And this is exactly what I would suggest you do: to try to figure out by yourself how it possibly can be done.
 
For those of you who want to read about it anyway...
The only website which I can't hold myself from telling you about is a website of a Russian-speaking Oleg Stepanov at http://stepanov.lk.net/. There you should click English flag to get the description in English language and then 'Mnemonics' button... At least this is the best website about mental math I know about!
Sure enough, you can also find a lot of information about this using search engine like www.google.com. By the way one of the reasons I advise you to do so is because as you well know websites are created and deleted all the time, and I don't want to give you a link to a site that is available at the moment of writing of these lines, and will not exist by the time you read my website.. Also, I don't want to limit you to only those sites that I can find myself now.