Choose any three by three square of dates on a calendar page...
Can you explain how this card trick works?
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.
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?