### Calendar Capers

Choose any three by three square of dates on a calendar page...

### Happy Numbers

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.

### The Patent Solution

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?

# Card Trick 2

##### Stage: 3 Challenge Level:

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 the table.

Volunteer then shuffles the pack of cards and returns them to me.

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 table.

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.