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?
On the planet Vuvv there are two sorts of creatures. The Zios
have $3$ legs and the Zepts have $7$ legs.
So naturally there are two forms of counting on Vuvv - Zios
count in base $3$ and Zepts count in base $7$.
When observed, the creatures on this planet lie on the ground
with their legs in the air, so that legs, not bodies, can be most
One day four of these creatures, two Zios and two Zepts, sat on
the summit of a hill to count the legs of the creatures they could
see. One looked to the East, one to the West, one to the South and
one to the North.
The creature looking to the West wrote down its number:
The creature looking to the East wrote down its number: $22$
The creature looking to the South wrote down its number:
The creature looking to the North wrote down its number:
In which direction are the $2$ Zios looking and in which
directions are the $2$ Zepts looking?