Books by Martin Gardner: Mathematics Magic & Mystery, Mathematical Magic Show, Encyclopaedia of Impromptu Magic etc. (Penguin)
Mathemagic by Royal Vale Heath (the classic!) (Dover)
Mathematical Magic by William Simon (Dover)
Arithmetricks series by Edward Julius (Wiley)
Mathematics Galore! by Budd and Sangwin (Oxford)
Magic Courses by Mark Wilson, Tarbell, Bill Tarr, Paul Daniels etc.
Memory Books by Harry Lorayne, Dominic O’Brien, David Berglas, Tony Buzan, Alan Baddeley
Self-Working Magic Series by Karl Fulves esp. Self-Working Card Magic (two volumes) and Self-Working Number Magic (Dover)
1.Evens & Odds
I invite two pupils, Nicole and Sean, up to the front and ask them to share 21 counters between them secretly. I then ask them to do a little calculation between them, and on hearing the result I am immediately able to say whether each child has an odd or an even number of counters!
Those of you who are quicker than me will have noticed that 21 is an odd number. That means that whatever the parity (oddness/evenness) of one child’s counters, the other child must be the opposite. This reduces the problem to finding out the parity of just one child’s counters. Let’s make it more specific by doing a calculation which will enable me to know which child holds the odd number.
I ask Nicole to double the number of counters in her hand and add the number of counters that Sean is holding. If the result is EVEN then Nicole must have had the odd number. If the result is ODD then Sean must have had the odd number.
To thunderous applause, Nicole and Sean return to their seats and we discuss why the trick works.
EVEN x EVEN = EVEN
EVEN x ODD = EVEN
ODD x EVEN = EVEN
ODD x ODD = ODD
EVEN + EVEN = EVEN
EVEN + ODD = ODD
ODD + EVEN = ODD
ODD + ODD = EVEN
As a follow up to this miracle, I ask Doris to come up and help. She takes some of the 21 counters but does not tell me. I count the rest and immediately tell her how many are in her hand. She is not impressed.
Persevering, I invite her to take some counters from the Big Bag Of Counters. Then I take some counters. I tell her that if she has an odd number I will make it even, and that if she has an even number, I will make it odd, just by adding all the counters in my hand. With great suspicion, she counts the counters in her hand and announces that it is an even number. Before she has a chance to see what is in my hand, I tip them all into her pile. Doris counts again, and now the number is odd, just as I had promised.
Just as she is going back to her seat, Doris turns round and looks at me with a big grin on her face. “I know how you did that!” she says, and she sits down smiling.
The 30-second “Countdown” theme is played (or similar) while the pupils quickly pass a Teddy round the class. When the music stops, Sameer is left holding Teddy. I ask Sameer to tell me the number of his house. He tells me that it is 46. Immediately I draw on the board the following square:
Quickly we add up each row: 46! And each column! The two diagonals as well!
The magic total 46 is obtained in every direction!
But then clever old Suraj and Emily have been adding in other ways. They point out that the corners add up to 46 too, and the 4 middle numbers! Before long the class has found that each corner 2x2 square totals 46, as well as the top/bottom half middle four. Later it is noticed that 1 + 12 + 27 + 6 = 11 + 5 + 2 + 28 = 46, and then Lateral Lisa pipes up with 1 + 11 + 28 + 6 = 12 + 2 + 5 + 27 = 46.