Always the Fourteenth!

Let’s take 27 cards out of a pack. Ask someone to take a card, to note which it is, and to replace it in the pack. With a little shuffling and manipulation, we can easily work out which it was.

Lay out the three columns, each containg nine cards face-up. Ask which column contains the card that was taken out. Gather the three columns together so that the column containing this card is in the middle of the pack. Again divide the pack into three columns of nine and ask which column contains the chosen card. Pick up the columns again, as before. Repeat this a third time.

Finally, count out 14 cards, the fourteenth being the card picked. The person will now be amazed and impressed. "Wow thats fantastic, you are just like David Cooperfield!!!!"

Is it magic? Or is it just pure mathmatics? Lets find out....

Fig.1

Before the first selection, the card is somewhere between 1 and 27 in the deck. When the person selects a column, it is narrowed down to between 10 and 18, because the selected column is put in the middle of the deck.

Fig.2

When the cards are laid out on the table the second time, the card is in either row 4, 5 or 6. When the person selects the column the second time, the position of the chosen card is either number 14, 15 or 16 in the deck, after the cards are but back in to the deck.

Fig.3

When the cards are laid out on the table the third and final time, the chosen card is in row 5. And when the person selects the column the last time, we know what card it is. And when we put the cards bakc in the last time with the selected column in the middle, the card is number 14. And then we count down to number 14 in the deck, from the top. The 14th card being the one picked. TADA!!

It was mathmatics, the magic of number 9!!