This activity investigates how you might make squares and pentominoes from Polydron.
If you had 36 cubes, what different cuboids could you make?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
You may have seen Magic Squares before, where each row, each
column and each diagonal adds to the same total. (Have a look at
the problem called
Magic Squares for an example.)
Here is a Polo Square:
You can see that eight numbers could be arranged in the Polo
Square - one in each box. In our Polo Square, the eight numbers can
be chosen from the counting numbers $0$ to $9$ inclusive. A number
cannot be used more than once. Each side of the Polo Square must
add to the same total - we can call this the Polo total.
Here is a partly completed Polo Square:
What is the Polo total?
Can you complete the Polo Square?
Can you find other ways of making a Polo Square with the same
What other totals are possible?
Is there more than one way of making each one?
Many thanks to Alan Parr for this investigation. Alan has
written several problem-solving maths adventures for 10 and 11
year-olds. The games are easy to use and very popular with
children. Details can be obtained from Alan at