A Mathematical Magic Trick
I will soon get back into some serious writing (I think). In the meantime, learn this card trick and amaze your friends/students/children.
STEP 1: Shuffle a full deck of 52 cards (no Jokers). As you shuffle, ask your volunteer how many cards are in a full deck (52). Then ask, "What's half of 52?" (26)
STEP 2: Hold the deck in your hands with all cards face up. Deal 26 cards face up, one on top of the other. You can count while you do this, or you can have your volunteer count. The most important part of this step, however, is to remember the seventh card (face/number and suit). When you finish this step, you should have two sets of cards—the cards that are in your hand and the face-up pile that contains 26 cards, including that key card (the seventh card you dealt).
STEP 3: Without putting down the cards that are in your hand, take the face-up pile, turn it over so that all the cards are facedown, and set it aside. Turn the cards in your hand over so that they are all facedown in your hand.
You'll probably want to explain the next step to your volunteer before proceeding. However, such an explanation is not essential. What you will be doing is creating three "columns" of cards. Each column will have a face-up card at the top and anywhere from zero to nine facedown cards under it. Face cards are worth 10, Aces are worth 1, and the number cards are worth their face value (2s are each worth 2, 6s are each worth 6, etc.). For each column, you will be "making tens" using this equation:
Face-up Card Value + Number of Facedown Cards = 10
STEP 4: Deal the top card in your hand face up. The value of this card is the first addend in the equation above. This value will determine the number of facedown cards you deal beneath it. For example, if you deal an 8 face up, then you will deal 2 facedown cards beneath it (8 + 2 = 10). If you deal an Ace face up, then you will deal 9 facedown cards beneath it (1 + 9 = 10). And if you deal a 10 or a face card face up, then you will not deal any facedown cards beneath it (10 + 0 = 10). The image below shows an example of what your first column might look like. Note that it is not important to keep the facedown cards separate, but it is important to keep the face-up card visible.
STEP 5: Deal the next card in your hand face up to create a second column. Again, use the equation above to determine the number of facedown cards to deal beneath it. Repeat this process to create the third column. The image below shows what your three columns could look like after you've finished. To create the columns shown below, I dealt an 8 face up to start the first column, then 2 facedown cards beneath it, a King face up for the second column, an Ace face up to start the third column, then 9 facedown cards beneath it.
STEP 6: Take the remaining cards in your hand and place them facedown on top of the pile that you set aside in Step 3. Pick up this pile and keep it facedown in your hand. Ask your volunteer to add up the face-up values in your three columns. In the example above, the sum would be 19 (8 + Ace + King = 8 + 1 + 10 = 19).
STEP 7: Deal the cards in your hand facedown, one on top of the other, and count the cards until you reach the sum found in Step 6. The last card you deal is that magic seventh card that you remembered way back in Step 2. In the example above, the 19th card would be the card that you remembered. Announce to your volunteer what this card is before turning it over.
I'll let you enjoy explaining the math behind this trick. And bonus points for finding the big flaw in this trick. And bonus bonus points if you can figure out a way to overcome said flaw.
STEP 1: Shuffle a full deck of 52 cards (no Jokers). As you shuffle, ask your volunteer how many cards are in a full deck (52). Then ask, "What's half of 52?" (26)
STEP 2: Hold the deck in your hands with all cards face up. Deal 26 cards face up, one on top of the other. You can count while you do this, or you can have your volunteer count. The most important part of this step, however, is to remember the seventh card (face/number and suit). When you finish this step, you should have two sets of cards—the cards that are in your hand and the face-up pile that contains 26 cards, including that key card (the seventh card you dealt).
STEP 3: Without putting down the cards that are in your hand, take the face-up pile, turn it over so that all the cards are facedown, and set it aside. Turn the cards in your hand over so that they are all facedown in your hand.
You'll probably want to explain the next step to your volunteer before proceeding. However, such an explanation is not essential. What you will be doing is creating three "columns" of cards. Each column will have a face-up card at the top and anywhere from zero to nine facedown cards under it. Face cards are worth 10, Aces are worth 1, and the number cards are worth their face value (2s are each worth 2, 6s are each worth 6, etc.). For each column, you will be "making tens" using this equation:
STEP 4: Deal the top card in your hand face up. The value of this card is the first addend in the equation above. This value will determine the number of facedown cards you deal beneath it. For example, if you deal an 8 face up, then you will deal 2 facedown cards beneath it (8 + 2 = 10). If you deal an Ace face up, then you will deal 9 facedown cards beneath it (1 + 9 = 10). And if you deal a 10 or a face card face up, then you will not deal any facedown cards beneath it (10 + 0 = 10). The image below shows an example of what your first column might look like. Note that it is not important to keep the facedown cards separate, but it is important to keep the face-up card visible.
STEP 5: Deal the next card in your hand face up to create a second column. Again, use the equation above to determine the number of facedown cards to deal beneath it. Repeat this process to create the third column. The image below shows what your three columns could look like after you've finished. To create the columns shown below, I dealt an 8 face up to start the first column, then 2 facedown cards beneath it, a King face up for the second column, an Ace face up to start the third column, then 9 facedown cards beneath it.
STEP 6: Take the remaining cards in your hand and place them facedown on top of the pile that you set aside in Step 3. Pick up this pile and keep it facedown in your hand. Ask your volunteer to add up the face-up values in your three columns. In the example above, the sum would be 19 (8 + Ace + King = 8 + 1 + 10 = 19).
STEP 7: Deal the cards in your hand facedown, one on top of the other, and count the cards until you reach the sum found in Step 6. The last card you deal is that magic seventh card that you remembered way back in Step 2. In the example above, the 19th card would be the card that you remembered. Announce to your volunteer what this card is before turning it over.
I'll let you enjoy explaining the math behind this trick. And bonus points for finding the big flaw in this trick. And bonus bonus points if you can figure out a way to overcome said flaw.
Labels: general, mathematics