South Carolina High Energy Mathematics Teachers' Circle Stacking a Deck of Cards

 You have ten cards numbered 1(ace), 2, 3, 4, 5, 6, 7, 8, 9, and 10. Your task is to arrange them in a particular order and put them in a stack, hold the stack in your hand, and then do the following: Put the top card on the table faceup. Put the next card on the bottom of the stack in your hand. Put the next card on the table. Put the next card on the bottom of the stack, and so on, continuing to alternate cards that go on the table and under the stack, until all ten cards are on the table. The trick: To lay the cards on the table in numerical order. The first card you put on the table will be number 1(ace), the next card you put on the table will be number 2, the next card you put on the table will be number 3, and so on, until the last card placed on the table will be number 10. In what order should the cards be arranged in the original stack so that this will happen? Here is an interesting variant: Start with all the cards in one suit in the deck: ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, and king. Arrange the cards in a particular order in your hand. Then spell the name of each card, putting one card on the bottom of the stack for each letter in the name of the card. For ace, you would say "A-C-E ace," putting three cards on the bottom of the stack and laying the fourth card faceup on the table (this card will be the ace). Then continue by saying "T-W-O two," putting three cards on the bottom of the stack and laying the fourth card (a 2) on the table just as you say "two." Continue in this way all the way through jack, queen, and king, each time ending the spelling by saying the card you just spelled as you lay it faceup on the table. What order do the cards have to be in originally for this to work out?