Cool Math Tricks: How to Impress Your Geeky Friends

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Cool Math TricksHow to Impress Your (Geeky)
Friends

• Ryo Takahashi

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Outline

• Finding out someones age
• Making huge magic squares
• Doing cube roots in your head

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Finding Out Someones Age

• If someone wont tell you his or her age, but you
  really want to know
• You can ask simple, innocent-sounding questions
  and determine their age if the person is
  gullible, he or she will just blindly answer all
  of your questions

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The Steps

• Have the person do the following
• Multiply the first number of your age by 5
• Add 3 to this number
• Double this number
• Add the second number of your age to this number,
  and reveal this number
• This number will be 6 more than their age

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Example

• Lets say someone is 37 years old
• You ask them to perform the mental calculations
• Multiply first number by 5 3 x 5 15
• Add 3 to this number 15 3 18
• Double this number 18 x 2 36
• Add second number 36 7 43
• Subtract 6 from 43, and youll get 37

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Why This Works

• Write the persons age as xy, so x is the tens
  digit, and y is the ones digit
• Then the persons age is 10x y

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Why This Works
5x 5x 3 10x 6 10x 6 y

• Multiply first number by 5
• Add 3
• Double this
• Add the second number
• This is exactly 6 more than their age

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Making Huge Magic Squares

• A magic square is an n x n matrix of numbers
  where each row, column, and diagonal add up to
  the same number
• Even a small 3 x 3 magic square can be hard to
  construct unless you know what it is beforehand

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Making Huge Magic Squares

• But with this trick, you can make any n x n magic
  square where n is odd

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The Process

• Put 1 in the square just right of the center
  square

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The Process

• Enter increasing numbers, moving diagonally
  upward to the right

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The Process

• Wrap around the edges of the box

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The Process

• If you hit a box thats already filled, continue
  numbering two squares to the right

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The Process

• Continue until the whole box is filled

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Huge Magic Squares

• In this way, you can make huge magic squares of
  odd dimension

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Huge Magic Squares

• What does each row, column, and diagonal add up
  to?
• The total of all numbers in the square is the sum
  of all numbers from 1 to n2, which is n2(n21)/2
• There are n rows, so each row adds up to
  (n2(n21)/2)/n same for columns and diagonals
• e.g. For the 9 x 9 square above, each row,
  column, and diagonal adds up to (92(921)/2)/9
  369

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Doing Cube Roots in Your Head

• Only for numbers lt1,000,000 Not very useful in
  real life
• but you can impress your friends!

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Demonstration

• Take any number less than 100 and cube it
• Tell me the cube and Ill tell you the cube root

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The Trick

• All you need to do for this trick is to memorize
  the cubes of 0-9

• 03 0
• 13 1
• 23 8
• 33 27
• 43 64

• 53 125
• 63 216
• 73 343
• 83 512
• 93 729

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The Trick

• By looking at where the number is in relation to
  the cubes of tens, we can figure out the tens
  place
• e.g. 405,224 lies between 703 343,000 and 803
  512,000, so the cube root must be 7_

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The Trick

• Neat fact Cubes of single-digit numbers all end
  in different numbers

• 03 0
• 13 1
• 23 8
• 33 27
• 43 64

• 53 125
• 63 216
• 73 343
• 83 512
• 93 729

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The Trick

• So by looking at the ones digit in the cube, you
  can determine the ones digit of the cube root
• e.g. 405,224 ends with 4, and 43 64, so the
  cube root must be _4
• Now you know the tens and ones digits, so you
  know the cube root

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Conclusion

• Using very basic math, you can impress people
• But this really only works on people who can
  appreciate the math
• But if they know too much, they wont be
  impressed theyll think these are just dumb
  tricks

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