Monday, 28 July 2008

A Fantastic Number 1001

Number 1001 is not just a number (in base 10).

It possess the ability to make any number that multiplies with it looks special.

Example: 123 x 1001

Answer becomes 123123.

Look at the pattern. The original number 123 repeats itself !

This property of number 1001 can be used to do maths trick.

We know that 1001 can be splitted into its prime number 7, 11, and 13.

With this knowledge,
- we can ask someone to come out with a 3-digit number (e.g. 135),
- ask him to repeat the number beside the original (135135)
- ask him to divide the number by 13,
- ask him to divide it again by 11, and lastly
- ask him to divide it by 7.

Without him telling you the answer, tell him your answer (135).
He will be very surprised!

You can customise the number of digits to other quantity also.

Why does the trick works?
By repeating the number besides the original, we are actually doing a 1001 multiplication.

abc(1001) = abc (100 + 1) = abc000 + abc = abcabc.

And by doing a division of 13, followed by 11, and 7, we are trying to do a division of 1001.

Therefore abc (1001) / 1001 gives us back the original abc.

Simple maths operations and its number theory can create interesting games and tricks that looks challenging at first. But with creativity and a bit of thinking, the answer to the maths puzzles can be easily realized.

By the way, this 1001 can be taken as binary ! (Not wrong)
It can then be used for other trick.

How can the number 1001 be 9?
Answer: By changing its base from 2 to 10!

Tricky? It is limited by our imagination.


1 comment:

RandomReflection said...

That is cool - I don't think I'd ever heard of that before but it is a great trick!