# Amazing Card Trick

## Problem

Amongst our trips was a second visit to the area around the island of Kekova (Turkey's largest, but quite small, island). The boat trip interspersed swimming and snorkelling with more intellectual activities including a look at the sunken city, views of Lycian tombs, and a trip to the medieval castle at Kaleucagiz. Last but not least, a sharing of card tricks with our tour guide Mehmet. My daughter and I showed Mehmet the Best Card Trick and in exchange he shared the following (amazing card trick) with us. Mehmet not only made the day memorable and enjoyable but left me with the problem of how the trick worked to solve. The mathematics is easy so I hope you will try to get to grips with it...........

Give a full deck of cards to someone in the audience and ask them to shuffle and cut them.

Take the pack face down and count out the first half of the pack, turning them face up onto a pile in front of the member of the audience.

When you have done this - pick up the 26 cards and place them face down back at the bottom of the pile you have in your hand.

Take three cards from the top of the pack and place them face up on the table. Then add enough cards to each (all face down) to make a total of 10.

So, if you turn up the 3

The three cards showing (face up) on the table are the 3

You should now be able to predict the 21st card down the rest of the pack sitting in your hand .

"And the 21st card will be..."

How is it possible to predict this card no matter what the three cards you turn over are?

Watch Charlie and Alison performing the Amazing Card Trick:

## Getting Started

Do you need to use any of the 26 cards that you turned up at the start of the trick?

Is this always the case?

## Student Solutions

Felix, Matthew, Alice, Robert, Hayden, Jenna, Catherine, James, James, Nick, Kieran, Kayleigh, Bethany, Luke and Matthew, all from Cupernham School sent in explanations which involved a similar argument. Correct explanations were also recieved from Andrei of School 205 Bucharest, Sophia of the Maths Club at Stamford High School and Matthew of Finley Middle School. Here is an explanation based on all of yours.

This card trick has nothing to do with magic, just mathematical thinking. When you do this trick, the total amount of cards on the table is 33.

It works because there are 3 cards you put down in the first place, the cards you add to them to make 10 and the number of cards down the pack. These make a total of 33 if you add them together. The number you memorise is the 7th card into the original half of 26. That is the top 26+7 into the original half equal 33 so that is how it works.

eg. If you lay down the 9 diamonds, 3 hearts and 6 clubs, it would look like this:

9 3 6 (three cards on the table)

You then lay down 1, 7 and 4 cards respectively (making a total of a12 +3 = 15 cards).

1 7 4

You then count down the pack 9+3+6 cards = 18 cards.

That is 15 cards on the table plus 18 cards down the pack- making 33.

9 3 6

-----

1 7 4

9 3 6

The 2 last rows show the cards that make up the original card to 10. These cards add up to 30. The top row is the original three cards, so if you add them on, the final total is 33. This is always true, because the three cards are made up to ten every time. This is because you have to make up the numbers on the cards, then deal out the original number again when you have made the prediction. The trick is when you deal out the 26 cards at the beginning, you take note of the 7th card. This is the card you predict.

If you do this trick properly it can be very entertaining!

## Teachers' Resources

Here is a silent video with written instructions for each phase of the trick. It can be displayed on a loop while students are figuring out the trick, to remind them of the instructions if they forget.