Fido the Magician
This week's resource is narrowinfocus but is offered just for fun...and surprise...and it can lead into a solid mathematics exploration.
Without a further intro, go to the Fido Puzzle. Do as it says, clicking on the lowerrighthand charater to move from frametoframe.
Be sure to test the trick using the following:
 2, 3, 4, 5, 6, ..., ndigit numbers. Does the trick always work?
 Try a case where you circle a zero obtained in the difference...what happens then? That is, does the person predict the right
digit? And if not, how is the predicted "wrong digit" a big clue...
 What happens if your initial number was 2222?
Now, try to determine how the trick is done by the magician, but not necessarily the underlying mathematics. My suggestion is to record your initial set of digits, the obtained difference, and the circled digit that was correctly predicted. A pattern is lurking here...!
Finally, why does this work mathematically? Note: This question is not trivial and will probably require some background in number theory.
