Magazine article Mathematics Teaching

# Mathemagic on the Motorway

Magazine article Mathematics Teaching

# Mathemagic on the Motorway

## Article excerpt

Carol Knights and Mike Ollerton discover that being stopped on a motorway can lead to a magical experience.

So there we were, stuck on the M6 between Birmingham and Manchester, travelling from one 'Rowland' venue to another. Mike sait! something ridiculous about Chichester being in Kent, and somehow we ended up at Mike Askew. Making a connection, Carol vaguely remembered an ATM conference opening adtlress at Ripon in 1994 (she doesn't get out much!) where Mike Askew had presented the following piece of Mathemagic...

* In the square grill above, choose a number, circle it and then cross out all other numbers in the same column as it, and then cross out all other numbers in the same row as it.

* From the remaining numbers, choose another, circle it and repeat the crossing out process.

* And another.

* You should onlv have one number left, circle it.

* Add the four circled numbers together.

What happens if you choose a different starting number?

Magic!

No peeping! Don't read beyond this bit if you haven't tried it.

The square grid is constructed as follows: Choose any values for a, h,c, d, w, x,y, and z.

The ''squareful' of magic is the 4-by-4 addition table without the a, b, c, d, w, x, y, z values arountl the edges.

For a particular 'squareful', why do you always get the same total?

How are these 'squareful' totals connected to vour initial values?

So once we'd got that one sorted, Mike posed a question about using products rather than sums. After exploring some maximum antl minimum value sums of 'squareful' products we decided there was nothing particularly special about them assuming we follow the same choosing antl crossing out process. …

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