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.
Explain why the arithmetic sequence
1, 14, 27, 40, ...
contains many terms of the form 222...2 where only the digit 2
appears. How many twos appear in these terms?