Choose any three by three square of dates on a calendar page...
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 combination mechanism for a safe comprises thirty-two tumblers
numbered from one to thirty-two in such a way that the numbers in
each wheel total 132... Could you open the safe?
Here are the instructions to a second card trick. This is also
mathematical. Try and explain how it works.
Volunteer selects any three cards and places them face down on
Volunteer then shuffles the pack of cards and returns them to
You are going to find a card in this pack which
depends on the three cards you have already chosen. I am going to
try and predict what card that will be. I am not going to alter the
order of the cards, I am just going to remove a card which points
to the card you will find.
Check the fourth from bottom card and remove the card of the
same numerical value and colour and place it face down on the
Volunteer turns over each of the three cards in turn and counts
onto 15 for each one. Remove the counted out cards each time. (Jack
=11 Queen =12 King =13)
The numbers of the three cards are added, and that number of
cards is counted out, the last one being kept.
Turn over that card and the predicting card.