### Calendar Capers

Choose any three by three square of dates on a calendar page. Circle any number on the top row, put a line through the other numbers that are in the same row and column as your circled number. Repeat this for a number of your choice from the second row. You should now have just one number left on the bottom row, circle it. Find the total for the three numbers circled. Compare this total with the number in the centre of the square. What do you find? Can you explain why this happens?

### Reverse to Order

Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?

### Card Trick 2

Can you explain how this card trick works?

# Card Trick 1

##### Stage: 3 Challenge Level:

Try this card trick it is mathematical. Can you explain (using mathematics) how it works? You might like to consider using some symbolism.

Here are the instructions:

Volunteer chooses 20 cards in the pack to turn face up.

Volunteer then shuffles the pack.

Volunteer removes the top twenty cards without me looking and the remainder are laid on the table.

The twenty cards are handed back to me, without me looking:

I dont know how many cards are reversed in this group I am holding, but it is likely to be less than the number in the rest of the pack. I like things to be balanced so I am going to try to turn some of the cards over so that both piles have the same number face up.

Turn the whole group upside down.

Count out the number which are face up in each pile. (they should both be the same!)