Magic does the trick

20th June 2008 at 01:00
Add some enchantment to your end of term maths lessons and you might see results materialise out of thin air, says Stephen Froggatt
Add some enchantment to your end of term maths lessons and you might see results materialise out of thin air, says Stephen Froggatt

Abracadabra. Say the magic word and suddenly maths is sprinkled with stardust. Why not try a few mathemagical gems on your pupils, bringing a sparkle to those end of term maths classes.

Think of a magic number

Ask everyone in the class to pick a number - any number. Add one. Take away their original number. They're left with: one.

OK, so perhaps that was not so mysterious (their teacher is obviously losing it). The next step is to ask everyone to write down a number between one and 20. Then double it, add 14 (pause and recap), then divide their answer by two. Does their teacher know what they've got? No. But ask them to take away their original number - and put up their hand if the answer is seven. Now they might be mildly impressed.


In this trick, cards appear in order simply by spelling out their names. I have five playing cards lying face down: five, three, two, ace and four, with the five on top.

I take one card from the top and place it underneath while I say "a". The next card goes to the bottom while I say "c". The third card follows while I say "e". Lo and behold, the next card is an ace. That goes on the desk.

Now I spell out the next number, t-w-o, using three more cards. The next card is a two. Five more cards spell out t-h-r-e-e, then four more spell f-o-u-r and the five is left in my hand. Can your pupils re-create the original order? (532A4). Can they do it with six cards? (425A36). The whole suit ace to king? (387AQ642JKT95).

This could lead older pupils into researching Monge, Faro and other specialised shuffles.

How do you get a spreadsheet to shuffle a pack of cards? By listing the cards in one column and random numbers in another, then sorting by the random number column. An interesting extension - why is there more than a 50 per cent chance that two shuffled packs have at least one matching pair somewhere through the two packs? (It's about derangements on n=52, giving p=0.632).


Get your pupils to produce 12 coins and count the ones with heads. Ask them to remember if this is even or odd. Get them to make seven coin turns - they can turn seven different coins, or one coin seven times, or a mixture - and count the heads again.

If the total was odd, it will now be even and vice versa. They could even cover one coin and you could tell if it was heads or tails.

Now ask why this works? (even + odd = odd, but odd + odd = even). Ask them what details of the trick can be altered without changing the result?

Stephen Froggatt is head of maths at Oaks Park High School in Ilford, Essex. There are more tricks on his website www.mathsisfun.netmagic.htm.

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