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!