Whats the Difference between a Magician and a Mathematician

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Whats the Difference between a Magician and a
Mathematician?

• Presented by
• Joe Hill
• Rockingham County Public Schools

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The difference is simple...

• Mathematicians and Magicians both like puzzles
  and tricks. So whats the difference?
• Magicians NEVER want you to know how their trick
  works
• Mathematicians ALWAYS want you to know how their
  trick works.

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Trick 1Guess the chosen card
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I know your card.

• On the next slide, youll see six cards.
• Your job is simply to pick one and memorize this
  card.

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Pick one
OK, now Ill shuffle and remove the card you
chose
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Removed yours, huh?
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One more time.pick one
OK, now Ill shuffle and remove the card you
chose
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Yours is gone!!
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The explanation for this trick is simple

• All eleven cards are different!
• In mathematical terms, the set of cards first
  shown to the viewer and the set of cards later
  shown to the viewer have no intersection.

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Trick 2Birthday Magic
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Magic Birthday
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Magic Birthday
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Magic Birthday
1
2
4
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Trick 3Whats Your Favorite Activity?

• Mines Math

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Favorite Activity...

• Ill take suggestions from the audience as to
  what your favorite activity is.
• Then well do some quick math to see what todays
  favorite is...

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Whats your favorite activity?
1
9
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8
3
7
4
6
5
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Follow these steps

• Choose a number (remember this number!)
• Add 2
• Multiply by 2
• Subtract the number you started with
• Add 5
• Subtract the number you started with again
• Count around the Favorite Activity chart

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Heres why it works

• Choose a number (remember this number!)
• Add 2
• Multiply by 2
• Subtract the number you started with
• Add 5
• Subtract the number you started with again
• Count around the Favorite Activity chart

• ?
• ?
• ? ?
• ?
• ?
• Notice that I put Math in the 9th spot!

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Trick 4Mind Reader!
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Mind Reader!

• On the next slide there are the numbers 0 to 99
  with a symbol below each.
• Choose a number 0 to 99. Lets call it X.
• Add the digits of the X. Call this sum Y.
• Subtract X - Y. Lets call this Z.
• Find Z on the chart and look at the symbol below
  it. This will be your final answer.
• Ill tell you what it is

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(No Transcript)
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One of these symbols was below your final answer
? _at_ gt lt
I think it was this one ?
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Well do it again with a different set of numbers
and symbols

• On the next slide there are the numbers 0 to 99
  with a symbol below each.
• Choose a number 0 to 99. Lets call it X.
• Add the digits of the X. Call this sum Y.
• Subtract X - Y. Lets call this Z.
• Find Z on the chart and look at the symbol below
  it. This will be your final answer.
• Ill tell you what it is

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(No Transcript)
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One of these symbols was below your final answer
lt ? ?
I think it was this one ?
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Heres how this one works
The reason this works is that, for any two digit
number, if you add the digits and subtract from
the original number you will end up with a
multple of 9. For example, 62 - 8 54. As
another example, 89 - 17 72. So the mystery
symbol is put under all multiples of 9. As a
proof, consider a two digit number x. Suppose
its digits are A and B. So x 10A B. x - (A
B) (10A B) - (A B) 9A, which is a
multiple of 9.
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Trick 5Magic Mental Addition
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I can add in my head faster than you can with a
calculator...

• Ill take three numbers in the range 1,000 to
  9,999 from the audience.
• Ill add a couple more to make the problem
  tougher.
• Then well add up the five huge numbersyou with
  a calculator and me in my head.
• Ill win.

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Trick 6How high can you multiply in your head?

• You did learn your multiplication facts through
  the 90s, didnt you?

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Amazing mental multiplication

• Pick any two numbers in the 90s.
• Multiply them together.
• I can do it in my headand so can you.

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Heres how its done
1. Determine how far each is from 100.

• Example
• 93
• x 96

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2. Multiply these two numbers together--this
will be the last two digits of your answer
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89
3. Subtract the SMALLER of the yellow numbers
from the SMALLER of the white numbers this will
be the first two digits of your answer.
Thanks to Scott Flansburg The Human Calculator
for this tip!
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One more example
1. Determine how far each is from 100.

• Example
• 89
• x 97

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2. Multiply these two numbers together--this
will be the last two digits of your answer
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86
3. Subtract the SMALLER of the yellow numbers
from the SMALLER of the white numbers this will
be the first two digits of your answer.
Algebra students--determine why this works!
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Heres the proof

• Suppose were multplying A x B. Let C 100 - A
  and D 100 - B (C and D are the yellow
  numbers). Suppose that A lt B so that A will be
  the smaller of A B which makes D the smaller
  of C and D. Note that A 100 - C
• A x B (100 - C)(100 - D)
• 10,000 - 100C - 100D C
• 100(100 - C - D) CD
• 100(A - D) CD
• Now you have it CD is the product of the two
  yellow numbers. This product goes in the last
  two digits of the answer. A - D is the
  difference between the smaller white number and
  the smaller yellow number. Multiplying by 100
  moves this difference over two places. Note that
  this process is good regardless of A and B but
  becomes cumbersome if A and B are not close to
  100.

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Trick 7Classroom puzzle

• Adapted from David Copperfields Orient Express
  Card Trick

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Classroom puzzle

• The next slide has a layout of various rooms in a
  school.
• You are allowed to move from one room to another
  one HORIZONTALLY and VERTICALLY only.
• Ill gradually take away rooms youre not
  currently in.

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Which Room Are You In?
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Which Room Are You In?
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Trick 8Betcha cant pick a number no one else
will choose...
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Be Different!

• Ill give an index card to every person in a
  group.
• You are to choose a whole number in the range 1
  to 100.
• Try to pick a number that NO ONE ELSE will pick
  and write it down.
• Bet you cant do it!!

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Which trick should I do next

• Pick one
• 1 2 3 4

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Why did you pick 3?
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Trick 9The Amazing Card Prediction Feat

• This is a complicated trick involving cards,
  dice, and addition.
• This trick cames from Richard Brown

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Part 1 Determine which card will be predicted

• Ill deal 20 cards to a person X.
• X will choose some of the cards--from 1 to
  10--and give them to Y.
• X then will count to see how many cards he has
  left (should be in the teens). Call this number
  N.
• X ADDS THE DIGITS of N and gives that many more
  cards to Y.
• X then counts to see how many cards he now
  has--this is the number of the card in the deck
  which will be predicted.

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Part 2 Determine the suit of the card

• Person Z will then be asked to pick a number from
  1 to 100.
• He will add that number to the next three higher
  whole numbers.
• Then hell divide by 4 and find the remainder.
• Remainder 1 means card is Diamond
• Remainder 2 means card is Club
• Remainder 3 means card is Heart
• Remainder 0 means card is Spade

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Part 3 Determine the face value

• Person W will then be given the dice and asked to
  roll them.
• The numbers which show up on top will be added to
  those which show up on the bottom.
• The result will be divided by 4.
• This answer is the face value of the card.

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How did that happen?

• In part 1, the answer will always be 9

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In part 2, the remainder will always be 2

• Four consecutive numbers will be as follows n,
  n 1, n 2, and n 3
• Their sum is 4n 6
• When 4n 6 is divided by 4 the remainder will be
  2
• So the suit of the card had to be clubs

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In part 3, the sum will always be 14

• On dice, 1 is always opposite 6 2 is opposite 5
  3 is opposite 4
• The sum of the dots on one dies top and bottom
  is 7 the sum on two dice will have to be 14
• So the division by 4 always turns out to give 3
  1/2 as an answer
• So I made a 3 1/2 of clubs out of a joker and
  buried it 29th in the deck (20 initial cards
  given out plus nine more)

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Trick 10Removing the vest without removing the
coat
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The Vest Trick...

• Ill put a vest on then put my coat on.
• Then Ill remove my vest without removing my
  coat.
• Youll see how its done as I do it.
• Where this trick came from will be a surprise.

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Remember Math isnt Magic

• Its just plain fun.