### 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?

# Back to the Planet of Vuvv

##### Stage: 3 Challenge Level:

Numbers are written by arranging digits in a row and each place in the row has a different value. This value depends on the base of the number system. The most common base nowadays is 10:

 10x10x10x10 10x10x10 10x10 10 1 Ten thousands Thousands Hundreds Tens Units/Ones

We often use these short forms for the columns:

 TTh Th H T U

To count in different bases, we just group numbers in a different way. For example, for base 2:

 2x2x2x2x2x2 2x2x2x2x2 2x2x2x2 2x2x2 2x2 2 1 Sixty fours Thirty twos Sixteens Eights Fours Twos Units/Ones

Zios count in base 3 so their numbers are grouped like this (we shall only look at the first three columns):

 3x3 3 1 Nines Threes Units/Ones

Let's work out what a Zio's 111 is in human numbers (base 10):

 Nines Threes Units/Ones 1 1 1

So, 111 = (1 x 9) + (1 x 3) + 1 = 13.

Zepts count in base 7 so their numbers are grouped like this:

 7x7 7 1 Forty nines Sevens Units/Ones

Let's see what a Zept's 111 is in base 10:

 Forty nines Sevens Units/Ones 1 1 1

So, 111 = (1 x 49) + (1 x 7) + 1 = 57.

To find out which way each type of creature is facing, calculate each number in human counting (base 10).

Remember that the creatures must be seeing numbers which could be a combination of Zios' and Zepts' legs.