The basic set up is:
- Ask the person to pick a card from a deck of 27 cards and remember it
- Shuffle it back into the deck
- Ask the person for their lucky number between 1 and 27.
You will deal the cards into three face-up piles exactly three times.
- Deal the cards one by one into three piles (left, middle, right)
- Ask the person which pile contains their card
- Collect the piles. The order in which you stack them (top, middle, or bottom) depends on the target number.
Show to the person that the card that they picked is positioned in their lucky number, starting from the top.
Can you explain the trick?
Explanation
To place the card at the exact target position, you must convert the person’s number into a base-3 sequence:
- Subtract 1 from their lucky number (e.g., if they chose 12, use 11)
- Represent that number in three digits using 0, 1, and 2
- 0 = Top
- 1 = Middle
- 2 = Bottom
- Use the digits from right to left (units, then 3s, then 9s) to determine where to place the person’s pile after each of the three deals.
Example:
If the person choose 15, you should subtract 1 from it:
14 in ternary is 112:
Deal 1: Put their pile on the Bottom (2).
Deal 2: Put their pile on the Middle (1).
Deal 3: Put their pile in the Middle (1).
The card will now be exactly the 15th card from the top.
Leave a Reply