Friday, March 1, 2013

Magic Square from Playing Cards


Blog-28

Dear Students,

I delivered the lecture on Mathematical Fun.  It was delivered in Indian Language “Marathi”. If you understand Marathi, Please click here to see my Lecture on youTube.

 

Secondly to think more about the studies of Mathematics, you are requested to participate in Program of Studies for Students and Parents given in my previous Blog (Blog-14).


Today we will see how to prepare the Magic Square from Playing Cards. This is very interesting topic of my eBook "Miraculous World of Numbers". We know that there are 52 cards in the deck of Playing Cards. 12 cards are Face Cards (King - K, Queen - Q, Jack - J) each of 4 types (Spades, Diamonds, Hearts & Clubs) and 4 types of Ace cards. Like this, all together we have 16 Cards (12 Face Cards & 4 Ace Cards. Making use of these 16 Cards, we will prepare the Magic Square of 4 by 4 (16) houses.

Please see the following diagram in which we arranged these 16 cards in such a way that each row & column has each card of each type. In short no card is repeated.




































Here 
A) 1st Row contain 1) King of Heart, 2) Ace of Diamond, 3) Queen of Club & 4) Jack of Spade.
B) 2nd Row contain 1) Queen of Spade, 2) Jack  oClub  3) King of Diamond & 4) Ace of Heart.
C) 3rd Row contain 1) Jack of Diamond  2) Queen of Heart  3) Ace of Spade & 4) King of Club.
D) 4th Row contain 1) Ace of Club  2) King of Spade  3) Jack of Heart & 4) Queen of Diamond.

Now we will allot numbers to Ace (A), King (K), Queen (Q), Jack (J), Heart, Diamond, Club, Spade as shown in the following diagram.








Now according to the places of the cards & the numbers allotted to these cards are placed at respective house of the Magic Square.

The card at 1st row & 1st column is King of Heart so its associated Number will be 26 so the Number in 1st row & 1st Column of the Magic Square will be 26 as shown in the following Diagram.

Similarly, 1st row & 2nd Column is Ace of Diamond so its associated number is 15 so in Magic Square 15 is written at the 1st row & 2nd Column and so on







Here the addition of the numbers in Each Row, Each Column & both the diagonals is 126.

In above Diagram, We used 15, 16, 17, 18, 25, 26, 27, 28, 35, 36, 37, 38, 45, 46, 47 and 48 as the Numbers obtained from the Card Numbers. Now we give 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 and 16 as the Reduced Numbers to above group and form the Magic square. It will be as shown bellow.

























Here the addition of the numbers in Each Row, Each Column & both the diagonals is 34.

Please put your comments about this BLOG & try for some new creation.

I thank Mrs. Jyoti Anil Satpute for designing all the diagram of my BLOGS & also of My forthcoming eBook "Miraculous World of Numbers. 

Anil Satpute