Challenge Level

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 Polo total?

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
alanparr@dial.pipex.com*