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Exploring Wild & Wonderful Number Patterns

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All Seated

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Found in the playground of a Danish school - something to sit on!

A 4x4 number square - starting top left 4 15 14 1 9 6 7 12 5 10 11 8 16 3 2 13 Look carefully at the numbers.

What do you notice?

Can you make another square using the numbers $1$ to $16$, that displays the same properties?

Find out what Albrecht Dürer has to do with this arrangement of numbers.

There are twelve different types of $4$ by $4$ magic square that use the numbers $1$ to $16$. See if you can find information about these twelve types and show examples of each one.

Look carefully in each case at the patterns produced when a total of $17$ is searched for.

Can you finish off the $5$ by $5$ magic square below?