This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
This activity investigates how you might make squares and pentominoes from Polydron.
If you had 36 cubes, what different cuboids could you make?
Try with a slightly simpler version: Starting with
ten cards numbered $1$ to $10$, can you arrange them in such a way
that - starting with the arranged pile face down - you can spell
out each card and reveal it as you announce its last letter?
Can you explain a way of doing this systematically so that you
can quickly arrange any number of cards to make the trick work?
And the really hard bit: What would happen if you
counted the number of cards equal to the value of the next card
(so, if the next card was due to be a six - you would put five
cards on the bottom of the pack and reveal the sixth)?