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?
Neda decided to take the ferry from the mainland to visit the four islands $P$, $Q$, $R$ and $S$.
The island $Q$ can be reached by ferry only from island $P$ or from the mainland. Ferries connect islands $P$ and $R$, and each of them with the mainland. Island $S$ only has a ferry connection with island $P$.
What is the smallest number of ferry journeys that Neda needs to take in order to visit all the islands and return to the mainland.
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
This problem is taken from the UKMT Mathematical Challenges.