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The Power of 2

The Power of 2. Starring: Kshitij (as Amar) Suhail (as Prem ). The Power of 2. 2 tricks with cards and coins that will seem “magical” but are “mathematical”. 2 magicians mathematicians, who will reveal the secrets behind both the tricks!

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The Power of 2

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  1. The Power of 2 Starring: Kshitij (as Amar) Suhail (as Prem)

  2. The Power of 2 • 2 tricks with cards and coins that will seem “magical” but are “mathematical”. • 2 magicians mathematicians, who will reveal the secrets behind both the tricks! • The number 2 is very “powerful”: small powers of 2 can yield really huge numbers. • For instance, the number 18,446,744,073,709,551,616 is simply 264.

  3. Plan kemutabiq… • Part 1: Demonstration (the magic show) • Part 2: Theory (how did that happen?) • Part 3: Practice (how can you do it?)

  4. Trick 1: Guess the fifth card(YaarPrem, zarabaharjana) • Audience picks five cards at random • Amar hides one of the cards with an audience member • Amar shows Prem the four remaining cards • Prem correctly guesses the (hidden) fifth card

  5. A Deck of Cards Four different suits (clubs, diamonds, hearts, spades) Thirteen cards of each suit (e.g. diamonds)

  6. An Example

  7. Premkinazron se • The suit of the fifth card is clubs • The number of the fifth card is ?

  8. How many ways to arrange A, 2, 3 ? +4 +1 +5 +2 +6 +3

  9. And the fifth card is… +2 =

  10. Arre Amar…

  11. What is the critical number? = - +2

  12. Finally, arrange A, 2, 3… +4 +1 +5 +2 +6 +3

  13. The cards are set

  14. Another Example

  15. What is the critical number? The critical number can only take values from +1 to +6 A 2 3 4 5 6 7 8 9 10 J Q K +2 The critical number is ?

  16. Join the ends A K 2 +4 Q 3 The difference between any two numbers on this circle is 6 or less J 4 5 10 6 9 +2 7 8

  17. The next three cards Any three cards can be ordered this way High: Mid: Low:

  18. Finally, arrange the next three cards In how many ways can you arrange three cards from left to right? High: Low: Mid:

  19. Premkinazron se

  20. The Procedure Amar • Select any two cards of the same suit for the first and fifth cards • If their difference in their numbers is 6 or less, make the smaller card the first card; otherwise make the larger card the first card • Arrange the remaining three cards to denote the critical number Prem • The suit of the fifth card is the same as that of the first card • The remaining three cards denote the critical number • If the sum of the first card and the critical number is 13 or less, then that sum is equal to the number on the fifth card; otherwise the number on the fifth card is 13 less than that sum

  21. What did we see? What will we see? • We start out with nonsense or seemingly useless information (you will see) • We cannot choose what information we want to convey • With very limited freedom, we convey the useful information (again, you will see) • We started out with nonsense or seemingly useless information (five random cards) • We chose what information we want to convey (fifth card) • With some amount of freedom (arrangement of cards), we conveyed the information

  22. Trick 2: Mark kidharhai ?(YaarPrem, zarabaharjana) • Audience randomly orients 32 cards face up/face down • An audience member puts an ‘X’ mark under one of the cards • Amar flips one of the cards • Prem correctly guesses the position of the (hidden) ‘X’ mark

  23. A Deck of Cards 0 1 2 3 4 5 6 7 8 9 10 11 13 14 15 12 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

  24. A Deck of Cards 00000 00001 00010 00011 00100 00101 00110 00111 01000 01001 01010 01011 01101 01110 01111 01100 10000 10001 10010 10011 10100 10101 10110 10111 11000 11001 11010 11011 11100 11101 11110 11111

  25. An Example X

  26. Premkinazron se

  27. Premkinazron se 5 1 6 10 11 16 21 28

  28. Premkinazron se 00101 00001 00110 01010 01011 10000 10101 11100

  29. Just add them up 0 0 0 0 1 Odd ≡One Even Zero 0 0 1 0 1 0 0 1 10 0 1 0 1 0 0 1 0 1 1 1 0 0 0 0 1 0 1 0 1 Mark idharhai 111 0 0 1 1 0 1 0

  30. Premkinazron se 00101 00001 00110 01010 01011 10000 10101 11010 11100

  31. Arre Amar… 00001 00110 01010 01011 10000 10101 X 11100

  32. Arre Amar… 0 0 0 0 1 If: Then: 0 0 1 10 0 1 0 1 0 0 1 0 1 1 1 0 0 0 0 1 0 1 0 1 111 0 0 Mark idharhai ? ? ? ? ? 11 0 1 0

  33. Arre Amar… 0 0 0 0 1 If: Then: 0 0 1 10 0 1 0 1 0 0 1 0 1 1 1 0 0 0 0 1 0 1 0 1 111 0 0 Mark idharhai 11 0 1 0

  34. Arre Amar… 0 0 0 0 1 If: Then: 0 0 1 10 0 1 0 1 0 0 1 0 1 1 1 0 0 0 0 1 0 1 0 1 111 0 0 Mark idharhai ? ? ? ? ? 11 0 1 0 0 0 1 0 1

  35. The cards are set 00001 00101 00110 01010 01011 10000 10101 X 11100

  36. Let’s have a big hand 4 2 8 1 6 1

  37. Hum sab meinkahiPremhai 26

  38. Thumb 26

  39. Index Finger 26

  40. Middle Finger 26

  41. Ring Finger 26

  42. Pinky Finger 26

  43. The Procedure • Thumb: Columns 2, 4, 6, 8 • Index Finger: Columns 3, 4, 7, 8 • Middle Finger: Columns 5, 6, 7, 8 • Ring Finger: Rows 2, 4 • Pinky Finger: Rows 3, 4

  44. A Bigger Deck of Cards 32 32

  45. Let’s have another big hand 4 1 2 8 6 4 2 5 6 2 8 1 5 1 6 2 3 2 1

  46. CRYPTOGRAPHERS Why ? We take inspiration from people that are experienced in dealing with useless information. Let’s consult the…

  47. Passing on a Secret • Prem needs to access Amar’s treasure, but there is a secret arrangement of levers (the password) that Prem needs to know. The password is:OFF OFF ON OFF ON OFF OFF ON(we write this as 00101001) • Amar can tell Prem this password, but there are other people who might be able to hear it.

  48. Secrecy • The only thing that Amar and Prem know, but nobody else knows is how Prem fared in his last 8 exams:PASS, PASS, PASS, FAIL, FAIL, FAIL, FAIL, PASS(we write this as 11100001) • This is not related to the password at all. • Yet, Amar can use this secret to tell Prem the password without other people figuring it out. • For this, he uses the flip function.

  49. The Flip Function: • Flipping nonsense with itself gives you nothing. • Flipping nothing with any data will not change the data. • If you start with nonsense, flipping it with itself and then flipping it with data will give you the data. • both erases the nonsense and adds the information we want. • Amar can just tell Prem to flip his exam results with and Prem will get the password, and nobody else will be able to get it. • Amar and Prem live happily ever after.

  50. Summary • Nonsense + nonsense sense • Anything that can be represented by two states can also be represented by binary numbers • Binary numbers have lots of tricks up their sleeves • The flip () is a very powerful tool for manipulating data • Now that you know the Why, let’s go have some Chai

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