Choose any three by three square of dates on a calendar page...
Can you explain how this card trick works?
Take any whole number between 1 and 999, add the squares of the
digits to get a new number. Make some conjectures about what
happens in general.
If you haven't already done so, take a look at the shaded image at the bottom of the problem.
If the bottom row is 6N, what can you deduce about the first digit of N?
If the fifth row is 5N, what can you deduce about the last digit in that row?
What can you say about the last digit of 2N, 4N and 6N?