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?
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?
Can you explain how this card trick works?
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:
We often use these short forms for the columns:
To count in different bases, we just group numbers in a
different way. For example, for base 2:
Zios count in base 3 so their numbers are grouped like this (we
shall only look at the first three columns):
Let's work out what a Zio's 111 is in human numbers (base
So, 111 = (1 x 9) + (1 x 3) + 1 = 13.
Zepts count in base 7 so their numbers are grouped like
Let's see what a Zept's 111 is in base 10:
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.