The Human Calculator

The key number for this trick is 142857. It is the only known number that never changes the rotation of its digits, except when that number is equally divided by the multiple of 7. For example: 1 x 142857 = 142857.

You must be capable of learning this formula:

2 x 142857 = 285714
3 x 142857 = 428571
4 x 142857 = 571428
5 x 142857 = 714285
6 x 142857 = 857142

This next number is the secret of the whole trick: 7 x 142857 = 999999.  So now you know that number is one less than a million. Your starting point for the trick is as follows. Lets say they say the number 12. You divide in your head 7 into 12 is one and 5 left over. The one becomes your first number in your answer followed by the 5th lowest number of the tricky number that turns out to be the number 7. So, starting with your 1 that we got by dividing is 171428 and because you started by adding 1 you subtract the 1 from the end that would be a 5 less 1 or the answer is 1,714284. So you call out say "your answer is one million seven hundred and fourteen thousand two hundred and eighty four".

Ask them to give you a number from one to a hundred and you do it again. For example, try number 31. Divide 7 into 31. Simple arithmetic is 4 and 3 left over. Your answer starts 4 with the 3rd lowest number that happens to be a 4. So your answer is 4,428,567. You arrive at the 67 ending by subtracting the 4 from the 71 ending. That gives you four million four hundred and twenty eight thousand five hundred and sixty seven.

Now this is the simplest of all if they give you a number equally divisible by 7. Lets try 42. Seven into 42 is 6. You know that every million is 1 less per million so your answer 5,999,994 and you say it to them as five million nine hundred ninety nine thousand nine hundred and ninety four.

The whole trick is really simple arithmetic. If you practice learning the sequences of 142857 for each of the 6 starting numbers, the rest will come easy. Try it on yourself and you should learn by doing. Once you get this formula tell me how you are doing with it.

I suggest you use your own calculator for practice, punch it all in, including the answer. Then, without looking at the answer, try it yourself. Then make the comparison if you made a mistake you can easier discover how the error was made.

Moe
moe@moesmagic.com