### Calendar Capers

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

### Card Trick 2

Can you explain how this card trick works?

### 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.

# Back to the Planet of Vuvv

##### Stage: 3 Challenge Level:

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 easily counted.

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: $122$

The creature looking to the East wrote down its number: $22$

The creature looking to the South wrote down its number: $101$

The creature looking to the North wrote down its number: $41$

In which direction are the $2$ Zios looking and in which directions are the $2$ Zepts looking?