Best Of Nine Card

Effect
It’s Open Evening and the hapless parents are being dragged round the Maths Is Fun
Department by their goggle-eyed offspring to play with all the games and puzzles on
display. I pick the parent who most clearly would prefer to be at home right now and
ask him to look at a pack of 9 cards which I have just dealt out from my shuffled
deck. I then ask him to take out his favourite and return the others face down to the
table. By now there is a little crowd forming around my desk, so he knows there is no
backing out now. Finally I ask him to show his card to a few others before placing it
on top of the other face down cards. I give the remainder of the deck a quick shuffle
and complete the pack. I thank the parent for his efforts, and promise that he has done
all the hard work. The rest of the trick will be done by the cards and some
devastatingly devious algebra.
Picking up the pack, I deal out the first card face up, saying “Ten!”. On top of that I
deal the second card “Nine!” and so on down to “One!”. I then place a face down
“lid” on that pile with one other card and repeat the process three more times, making
4 piles altogether.
If a face up card appears with the same number as the one I am saying then I stop and
move on to the next pile, starting again from “Ten!”. “These cards seem to be telling
me something” I mutter mysteriously.
When the last pile is complete, I have some cards in my hand. On the table in front of
me are some face up cards, let’s say they are a 3 and a 5. (“They are a 3 and a 5!”) I
now add these numbers together and count down to the eighth card in my hand. It is,
of course, the parent’s card. Pumping his hand vigorously, I thank him for his time,
and explain that Maths really does have many surprising uses.
Method
Johnny Ball named this trick as his favourite card trick of all. It is completely selfworking,
and the underlying algebra is certainly accessible to school children.
When I place the balance of the deck on top of the spectator’s pile of nine, it makes
his card 44th from the top (with 8 below it). The fancy counting is just doing 4 x 11.
If there are no matches, then the final “lid” is the spectator’s card, but this rarely
happens. If I stop part way through, then the number on display tells me how many
cards are missing from the intended 11.
If there are n cards in the pile then I need (11-n) to complete it.
As I deal the nth card I am saying the number (11-n), and the number (11-n) is on
display if I get a match.
After dealing four piles in this way, the cards needed to complete each pile are still in
my hand. Adding the face up cards is equivalent to placing them back on their piles,
and the final card is therefore the 44th card. I usually ask the spectator to name his
card first. “Seven of hearts” he says. “Not this seven of hearts by any chance?” I ask,
as I turn over the final card.
Most packs of cards in school have a few cards missing. If this is the case, then just
subtract the number of missing cards from the 9 in the introduction.