A to 10 card trick

Thanks to Barasa in Kenya for telling us about this one …

Challenge 1

Take 10 cards from a deck – A,2,3, … 10. Ace represents 1.

Arrange the cards in a pile face down so that when you show the first card it is the Ace. Remove this card. Then count to two putting the first card on the bottom of the pile. The second card should be the two. Show it and remove it. Then count to three, each time you say a number you should be putting a card on the bottom and then when you get to 3 you show the 3 and remove it from the pile.

Arrange the cards so that this works for every number from A to 10. By the time you get to 9 you should only have two cards left in your hand! Cycle through them counting 1, 2, 3, … 9 and show the 9. And then you just have 10 left and the trick is over.

Challenge 2

Try to arrange the cards to perform the same trick except you don’t remove the card when you show it. The card is just placed at the bottom of the pile and you start counting the next number.

You should find out that this is impossible for 10 cards. Is there a number of cards that it would work for?