# Maths Busking, maths through street performance since 2010

#### Magic Squares

The busker can produce a Magic Square, whose rows and columns add up to any number you suggest!

How does this work?

There are many ways to produce an instant magic square, and this is a simple method (which is a bit of a cheat!) The busker has memorised the layout of the numbers one to twelve in the grid, as seen here:

Then the remaining squares are filled in using your number: the top left square is found by subtracting 20 from your number, and the rest are filled in as shown here:

This magic square, as well as having all rows and columns and both diagonals sum to your total, also has many other combinations of four squares which add up to your total. For example, the 2x2 squares in the corners; the corners of any 3x3 square in the grid; and also, two diagonal rectangles whose corners add up to your total. Can you find all 36 combinations?

#### References

Martin Gardner,

*Mathematical Puzzles
and Diversions*,

Penguin Books, 1991