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.
A bag contains 12 marbles. There are more red than green but
taking the green and blue together exceeds the number of reds. The
total number of yellow and green marbles is more than the total
number of red and blue. Find exactly how many of each colour there
are in the bag. How many different solutions can you find?