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.
Ann thought of 5 numbers and told Bob all the sums that could be
made by adding the numbers in pairs. The list of sums is 6, 7, 8,
8, 9, 9, 10,10, 11, 12. Help Bob to find out which numbers Ann was
[This is an exercise for practice from the Hungarian KöMaL
magazine, September 2000 issue. You'll find many other challenging
problems in English on the KöMaL