Effect

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!

Method

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.

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.