Card Mathematical Intelligence Games

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Author: Adekola Taylor
November, 2013

Introduction

If magic is the use of intelligence in form of tricks, deception or strategies to produce mysterious, amazing and mind-blowing results then card mathematical magic can be defined as the use of mathematical intelligence in form of card tricks or strategies to produce mysterious, amazing and mind-blowing results. The novelty of card mathematical intelligence game tricks is that they are based on simple mathematical principles. The principles underlying card mathematical intelligence game tricks were coined out from distributive regeneration of ordered system (Taylor, 2013).

Interestingly, mathematical formulas can also be used to work out the transposition of elements (objects) from one distribution to another. Distributive Regeneration of Ordered System is a phenomenon that was discovered during a research on some of the mathematical card tricks. Distributive Regeneration of Ordered System is a phenomenon which occurs when a given system of order comprising a number of elements (cards) that are grouped into two or more columns and rows is subjected to a Logico-Sequential Distribution for the purpose of regeneration (Taylor, 2010).

CMIG TRICK ONE

Deal out 42 cards face down into a grid of 6 columns and 7 rows. Do this by dealing out 6 cards horizontally in a row, then 6 more cards just above the first 6, then 6 more, etc., until you have 7 cards in each column. Discard the remaining cards. Only these 42 cards would be used to play. Ask a spectator to take a card out of the 42 cards without making you to see the face of his chosen card. Collect the remaining 41 cards into a deck.

With the spectator's card in his hand, deal out the remaining cards face down into 6 columns and 4 rows. In other words, each column is having 4 cards. Ask the spectator to put his chosen card with its face down on the first column without making you to see the face of his chosen card. Afterward, deal out the remaining 17 cards, starting from the second column to the sixth column, then back to the first column to the sixth column until you have 7 cards in each column.

Collect the 42 cards into a vertical column, with cards in column 1 at the top, followed by cards in column 2, followed by cards in column 3, column 4, column 5 and cards in column 6 at the bottom. Deal out all the 42 cards into 6 columns and 7 rows, starting from the topmost card to last card at the bottom.

Again collect the 42 cards into a vertical column as described above. Repeat the whole process of dealing out of the 42 cards until you have done 4 dealing out without any disruption. After the 4 dealing out, gather all the cards into a single vertical column as usual, and then the spectator's chosen card would be at 25th position counting from top downward. The spectator's card would now be the 25th in the deck.

Having known these facts spread the cards on the table by counting them mentally. Make sure you don't mix his chosen card with the rest of the cards. You can now give the spectator his chosen card; if you like you can put on a kind of abracadabra display to further amaze and daze your spectators.

CMIG TRICK TWO

Hand over 12 cards to a spectator; tell him to mentally pick a card out of the 12 cards. Collect the cards from him. Deal out 12 cards face down into a grid of 3 columns and 4 rows. Do this by dealing out 3 cards horizontally in a row, then 3 more cards just above the first 3, then 3 more, etc., until you have 4 rows.

Instruct the spectator to look for his mentally picked card. Ask him to tell you which of the 3 columns it is in. If the column containing his mentally picked card is not in the middle column, make rearrangement; shift it to the middle column such that the column containing the spectator's is second. Collect the 12 cards into a deck vertically, column by column from column one to column three respectively.

Pick up cards from the top of the column to the bottom, keeping them in the same order and deal them out again into a grid of 3 columns and 4 rows as explained above. Again, ask him to search and tell you only which column contains his mentally picked card. If the column containing his mentally picked card is not in the middle column, make rearrangement; shift it to the middle column such that the column containing the spectator's is second. Collect the 12 cards into a deck vertically, column by column from column one to column three respectively.

Repeat the whole process until you have done 3 Logico-Sequential Distributions, after that make the final rearrangement. Gather all the cards into a single column as usual. The spectator's mentally picked card would be at either 7th position or 6th position counting from top downward.

Spread the cards on table with their faces down while doing this; separate the two cards occupying the positions 7th and 6th. Tell the spectator to pick and look at one of the two separated cards. Ask him: "Is that your chosen card? If he says NO, then the second card is his mentally picked card. If he says YES, then you have done a greater amazement.

CMIG TRICK THREE

Hand over 30 cards to a spectator; tell him to mentally pick a card out of the 30 cards. Collect the cards from him. Deal out 30 cards face down into a grid of 3 columns and 10 rows. Do this by dealing out 3 cards horizontally in a row, then 3 more cards just above the first 3, then 3 more, etc., until you have 10 rows.

Instruct the spectator to look for his mentally picked card. Ask him to tell you which of the 3 columns it is in. If the column containing his mentally picked card is not in the middle column, make rearrangement; shift it to the middle column such that the column containing the spectator's is second. Collect the 30 cards into a deck vertically, column by column from column one to column three respectively.

Pick up cards from the top of the column to the bottom, keeping them in the same order and deal them out again into a grid of 3 columns and 10 rows as explained above. Again, ask him to search and tell you only which column contains his mentally picked card. If the column containing his mentally picked card is not in the middle column, make rearrangement; shift it to the middle column such that the column containing the spectator's is second.

Collect the 30 cards into a deck vertically, column by column from column one to column three respectively. Repeat the whole process until you have done 3 Logico-Sequential Distributions after that make the final rearrangement. Gather all the cards into a single column as usual. The spectator's mentally picked card would be at either 15th position or 16th position counting from top downward.

Spread the cards on table with their faces down while doing this; separate the two cards occupying the positions 15th and 16th. Tell the spectator to pick and look at one of the two separated cards. Ask him: "Is that your chosen card? If he says NO, then the second card is his mentally picked card. If he says YES, then you have done a greater amazement.

CMIG TRICK FOUR

Hand over 39 cards to a spectator; tell him to mentally pick a card out of the 39 cards. Collect the cards from him. Deal out 39 cards face down into a grid of 3 columns and 13 rows. Do this by dealing out 3 cards horizontally in a row, then 3 more cards just above the first 3, then 3 more, etc., until you have 13 rows.

Instruct the spectator to look for his mentally picked card. Ask him to tell you which of the 3 columns it is in. If the column containing his mentally picked card is not in the first column, make rearrangement; shift it to the first column. Collect the 39 cards into a deck vertically, column by column from column one to the third column respectively.

Pick up cards from the top of the column to the bottom, keeping them in the same order and deal them out again into a grid of 3 columns and 13 rows as explained above. Again, ask him to search and tell you which column contains his mentally picked card. If the column containing his mentally picked card is not in the first column, make rearrangement; shift it to the first column.

Collect the 39 cards into a deck vertically, column by column from column one to column three respectively. Repeat the whole process until you have done 3 dealing out or more. After that, gather all the cards into a single column as usual, and then the spectator's mentally picked card would be at 10th position counting from top downward. The spectator's card would now be the 10th in the deck.

CMIG TRICK FIVE

Deal out 32 cards face down into a grid of 2 columns and 16 rows. Do this by dealing out 2 cards horizontally in a row, then 2 more cards just above the first 2, then 2 more, etc., until you have 16 cards in each column. Discard the remaining cards. Only these 32 cards would be used to play. Ask 3 spectators to take a card each out of the 32 cards without making you to see the face of their chosen cards. Collect the remaining 29 cards into a deck.

With the spectators' cards in their hands, deal out the remaining cards face down into 2 columns and 4 rows. In other words, each column is having 4 cards. Ask the first spectator to put his chosen card with its face down on the first column without making you to see the face of his chosen card. Afterwards, deal out one card on the second column to make 5 cards per column.

Again deal out three cards each on the columns to make 8 cards per column. Ask the second and the third spectators to put their chosen cards on the first and second columns respectively to make 9 cards per column. Afterward, deal out the remaining 14 cards, starting from the first column to the second column until you have 16 cards in each column.

Collect the 32 cards into a vertical column, with cards in column 1 at the top, followed by cards in column 2 at the bottom. Deal out all the 32 cards into 2 columns and 16 rows, starting from the topmost card to last card at the bottom. Again collect the 32 cards into a vertical column as described above.

Repeat the whole process of dealing out of the 32 cards thrice without any disruption. After the dealing out, gather all the cards into a single vertical column as usual, and then the first spectator's chosen card will be at 9th , the second and the third spectators'cards would be at 17th and 18th positions respectively counting from top downward.

Having known these facts spread the cards on the table by counting them mentally. Make sure you don't mix his chosen card with the rest of the cards. You can now give the spectator his chosen card; if you like you can put on a kind of abracadabra display to further amaze and daze your spectators.

The Mathematics behind CMIG TRICK TWO (Taylor, 2012)

Four Steps to follow:

  • Order the cards with all their faces down.
  • Designate each card with a specific number.
  • Tell the spectator to put his chosen card in your predetermined horizontal position.
  • Using Logico-Sequential Distribution, distribute the cards.

n(E) = Total Number of Cards = 12, C = Total Number of Columns = 3, r = Total Number of Rows = 4

Let the first card you put in column 1 be designated by number 1, the first card in column 2 be designated by number 2, the first card in column 3 be designated by number 3, the second card in column 1 be designated by number 4, the second card in column 2 be designated by number 5, the second card in column 3 be designated by number 6 etc as shown in the table for CMIG Trick 2.

Let the mentally picked card of the spectator be the card designated by number 9, let Rx represents number of rearrangements and let dx represents number of Logico-Sequential Distributions. Let Rf represents final rearrangement. Remember the column containing the spectator's card must always be in the middle column before distribution. This is what necessitated rearrangement.

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Considering the figure above, if all the cards at Rf (the final rearrangement) are gathered into a single column as usual, then the spectator's mentally picked card would be at 7th or 6th position counting from top downward. The spectator's mentally picked card will be at either 6th position or 7th counting from top downward.

Spread the cards on table with their faces down while doing this; separate the two cards occupying the positions 6th and 7th. Tell the spectator to pick and look at one of the two separated cards. Ask him: "Is that your chosen card? If he says NO, then the second card is his mentally picked card. If he says YES, then you have done a greater amazement. In this case the spectator's mentally picked card is at 6th position counting from the top downward. This is the diagrammatic representation of what all that is happening behind the scene during demonstration.

References

  1. Taylor, Adekola A. (2016). Derivation of formulas for position change of entities in power inductive distribution. International Journal of Scientific and Research Publications 6(7):409-420.

  2. Taylor, Adekola A. (2015). Quadratic distribution patterns in Kola analysis. Mathematical Theory and Modeling 5: 60-66.

  3. Taylor, Adekola A. (2015). Derivation of formulas for position change in Kola analysis. International Journal of Scientific and Research Publications 5(11):101-109.

  4. Taylor, Adekola A. (2014). Logical-mathematical intelligence for teens. Mathsthoughtbook.com

  5. Taylor, Adekola A. (2013). Regenerative mathematics and dimurelo puzzles for children 8-12yrs. USA: Lulu Press Inc.

  6. Taylor, Adekola (2013). Card magic and my mathematical discoveries. USA:Lulu Publishing.

  7. Taylor, Adekola A. (2010). Kola Analysis: An inventive approach to logical-mathematical intelligence for secondary and advanced levels. Journal of Mathematical Sciences Education 1(1): 44-53.<

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