- When you’re ready, go to the link here.
- After reading and carrying out instructions in each window, click on the boy in the lower right corner of the picture.
- In the last window type in your answer in the white box using the keyboard (there is NO cursor).
- Watch the paper in the boy’s hand. You will be amazed and no, I don’t know how it’s done.
This entry was posted on Tuesday, January 15th, 2008 at 6:51 am and is filed under Miscellaneous. You can follow any responses to this entry through the RSS 2.0 feed. Responses are currently closed, but you can trackback from your own site.
January 15th, 2008 at 10:09 pm
OMG! that is kinda spooky. i wonder how its done.
January 15th, 2008 at 10:32 pm
Brilliant!
January 16th, 2008 at 11:41 am
It works in a similar manner to this: The Flash Mind Reader.
Quantum mechanics permits synchronicity of thought and computer software. Clearly the thought vibrations in the brain are communicated, by means of quantum entanglement, to the server running the program.
Quite incredible!
January 16th, 2008 at 5:11 pm
A clever friend has helpfully provided this answer:
his trick uses the following facts (which I won’t rigorously prove — see e.g. Digital Root).
1. If you rearrange the digits of a number, and subtract one from the other, the result is always a multiple of 9.
2. The sum of the digits of any multiple of 9 is itself a multiple of 9.
These facts tell us that when we’ve subtracted one number from its rearrangement, the sum of the digits in the answer will be a multiple of 9. This allows the program to determine the missing number.
Example: 5743 – 3547 = 2196. Suppose you select 2, and type 691. The sum of these three digits is 16. The program knows that the sum of all the digits is a multiple of 9, which in this case must be 18. That leaves 2 as the missing digit.
Notice that if we’d selected 9, and typed 621, the sum of the three digits would have been 9. Now the missing digit could be either 0 or 9. But, in a clever touch, the trick asks us not to circle a 0!
So why is the difference between the two numbers always divisible by 9? There are various ways to see this. As an example, consider abc – cab. In full, this is:
(100a + 10b + c) – (100c + 10a + b) = 90a + 9b – 99c = 9(10a + b – 11c).
The difference is divisible by 9 because each term — 90a, 9b, 99c — is divisible by 9. And each term is divisible by 9 because it is of the form 10^r – 10^s. A power of 10 can always be written as 10^r = 1 + 9999…9, with r 9s. For example, 10^3 = 1 + 999. That is, as 1 plus a number divisible by 9. So when you subtract one power of 10 from another, the 1s cancel, leaving you with a number divisible by 9.
If you’ve studied modular arithmetic, you’ll know that the above can be expressed more compactly in terms of congruences, modulo 9.
So now you know …