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.
This problem has too many cases for a trial and error method, so here are some questions to help you get started.
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?
Below is a possible order in which you can work out each value (cell a first, then cell b, and so on...)