# Math Tricks for All Ages

### This web page is devoted to the

incredibly boffo

idea that math can be fun!

### Try these tricks:

## Here are some interesting links:

- A Reading list of Tricky Math Books, most of which I have used for this site.
- Learn about the original computer: The Abacus (http://www.ee.ryerson.ca:8080/~elf/abacus/)
- Play a Math-Chase Game (http://dev.eyecon.com/marcia) — for one or two players. (If you’re using Netscape,
**Do Not Scroll down the page while this loads**. - Play at Shoot Balls (http://www.fi.uu.nl/wisweb/en/applets/bollen/Welcome.html).
- Play Flippo 24 (http://www.fi.uu.nl/wisweb/en/applets/bollen/Welcome.html).
- Test your knowledge of the multiplication tables (http://www.fi.uu.nl/wisweb/en/applets/tafels/Welcome.html)
- Try your hand at estimation (http://www.fi.uu.nl/wisweb/en/applets/bollen/Welcome.html).
- Explore Geometryin a fun and interactive way.
- Try the Tower of Hanoi Puzzle (http://www.eng.auburn.edu/~fwushan/Hanoi1.html).
- See what a Spriographis (http://www.mainstrike.com/mstservices/handy/Spiro/).
- See what a Mandelbrot setis (http://www.franceway.com/java/fractale/mandel_b.htm).
- If you want more math challenges try the new PBS MATHLINE MATH CHALLENGESsite. Try it, you’ll like it. (But remember we were first.)

## Magic Addition Trick #1

Amaze the peons with this matchless. It ‘s elementary. It ‘s effective. It gets them every time .

- Ask your mark to pick three (3)
**different**numbers between 1 and 9. - Tell him or her (or her or him) to write the three numbers down next to each other, largest first and smallest last, to form a single 3-digit number. Tell him/her not to tell you what the numbers are.
- Next have her or him form a new 3-digit number by reversing the digits, putting the smallest first and the largest last. And write this number right underneath the first number.
- Now have him or her subtract the lower (and smaller) 3-digit number from the upper (and larger) 3-digit number. Tell them not to tell you what the result is.
- Now you have a choice of wrap-ups:
- Ask your friend to add up the three digits of the number that results from subtracting the smaller from the larger 3-digit number. Then amaze him or her by teling them what the sum of those three numbers is. The sum of the three digit answer will always be 18!
- Tell your friend that if she or he will tell you what the first OR last digit of the answer is, you will tell her or him what the other two digits are. This is possible because the middle digit will always be 9, and the other two digits will always sum to 9! So to get the digit other than the middle one (which is 9) and other than the digit that your friend tells you, just subtract the digit your friend tells you from 9, and that is the unknown digit.

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## Magic Square #15

Every rowing and column sums to 15 in this magic square. thus do both diagonals !

8 | 3 | 4 |

1 | 5 | 9 |

6 | 7 | 2 |

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## Magic Square #34

Every rowing and column sums to 34 in this magic trick square. so do both diagonals !

1 | 15 | 14 | 4 |

12 | 6 | 7 | 9 |

8 | 10 | 11 | 5 |

13 | 3 | 2 | 16 |

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## A Recipe for Your Own 3 X 3 Magic Square

here ‘s a recipe for making your own 3 X 3 charming number squarely. This recipe and both of the above two magic squares comes from one heck of a great reserve called, Mathematics for the Million, by Lancelot Hogben, published by Norton and Company. I highly recommend it. You do n’t need much mathematics at all to get into the gamble of numbers told in this classic koran .

Some necessary rules and definitions :

- Let the letters a, b, and c stand for integers (that is, whole numbers).
- Always choose a so that it larger than the sum of b and c. That is, a > b + c. This guarantees no entries in the magic square is a negative number.
- Do not let 2 X b = c. This quarantees you won’t get the same number in different cells.
- Using the formulas in the table below, you can make magic squares where the sum of the rows, columns, and diagonals are equal to 3 X whatever a is.

a + c | a + b – c | a – b |

a – b – c | a | a + b + c |

a + b | a – b + c | a – c |

To create the first Magic Square # 15 above, you let a be peer to 5, let b be equal to 3, and let carbon be peer to 1. here are some others :

- a = 6, b = 3, c = 2
- a = 6, b = 3, c = 1
- a = 7, b = 3, c = 2
- a = 7, b = 4, c = 2
- a = 8, b = 6, c = 1
- a = 8, b = 5, c = 2
- a = 8, b = 4, c = 3

Try making up some of your own .

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## Upside Down Magic Square

here ‘s a magic trick square that not only adds up to 264 in all directions, but it does it even when it ‘s top down ! If you do n’t believe me, look at it while you are standing on your head ! ( Or, precisely copy it out and turn it top down. )

96 | 11 | 89 | 68 |

88 | 69 | 91 | 16 |

61 | 86 | 18 | 99 |

19 | 98 | 66 | 81 |

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## Anti-magic Square

here ‘s a magic trick square with a many different totals as potential .

5 | 1 | 3 |

4 | 2 | 6 |

8 | 7 | 9 |

This mesa produces 8 different totals .

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## Win Bets with this Magic Square

OK, here ‘s a clean way to win bets with a magic public square. Call a friend on the call. Have him or her get a pencil and paper and bring it to the earphone, so he or she can write down numbers from 1 to 9. Tell your friend that you will take turns calling out numbers from 1 to 9. Neither one of you can repeat a total that the other one calls out. Both of you then write down the numbers 1 to 9. then when your friend says one of the numbers he or she draws a circle around that numeral, and therefore do you. When you say a number, you draw a square around that count, and so does your friend. The winner is whoever is the first one to get three numbers that add up precisely to 15 .

Say you go first and you call out 8. Your friend might call out 6. You then call out 2. Your friend calls out 5, and you call out 4. Your ally calls out 7, and you call out 3. then you tell your friend that you have fair won because you called out 8, 3, and 4, which add up to 15 .

Your ally will want to play again. So this time you can bet him you ‘ll win, with the circumstance that in font of a draw ( where you use up the numbers 1 to 9 without either of you getting a 15 entire ) cipher owes anything .

If you know the trick, you will never lose, and will probably will most times .

**The tricks** actually the trick is based on both ticktacktoe and a magic trick square. The charming hearty look like this :

8 | 1 | 6 |

3 | 5 | 7 |

4 | 9 | 2 |

Because this is a magic square, every quarrel and every column and every diagonal adds up to 15. then if you ‘ve got this square in front of you with your ally on the phone, you can put an adam in the squares of the number you call out, and an O in the squares of the numbers your ally calls out. then, just like in ticktacktoe, you try to get three X ‘s in a course, because those will always add up to 15 .

so in the model above, when you call out 8, you put an ten in the upper leave corner. When your ally says 6, you put an ) in the upper right corner. And then on .

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## Mathematical Card Trick

You need an ordinary pack of cards for this wower. No illusion shuffle is required. fair follow these easy steps :

- Shuffle the cards to mix them thoroughly.
- Deal out 36 cards into a pile.
- Ask a friend to pick one of the 36 cards, look at it and memorize it, and then put it back in the pile without letting you see it.
- Shuffle the 36 cards.
- Lay the 36 cards out in 6 rows of 6 cards each. Be sure to deal the top row from left to right. Then deal the second row beneath it from left to right. And so on with each succeeding row laid out underneath the one before.
- Ask your friend to look at the cards and tell you which
**row**the chosen card is in. Remember what number the row is. - Carefully pick the cards up in the same order you laid them down. So the first card on the left of the top row is on top of the stack, and the last card on the right of the bottom row is on the bottom of the stack.
- Now lay the cards down in 6 rows of 6 cards each, but this time spread the card one column at a time. Instead of proceeding from one row to the next, proceed from one column to the next. Lay the first six cards in a column from top to bottom on the far left. Then lay out the next six cards in a second column of six cards just to the right of the first column of six cards. Continue doing this until you have 6 columns of 6 cards each (which looks the same as 6 rows of 6 cards each — because it is the same).
- Once again ask your friend which row contains the chosen card.
- When you friend tells you which row the card is in, you can say what the exact chosen card is. How? If your friend said the card was in row 2 the first time, and in row 5 the second time, then the chosen card is the one in the second column of the fifth row. This is because the way you arrange the cards, what were rows the first time around become columns the second time around.

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## Lightning Calculator

hera ‘s a flim-flam to wow them everytime ! Have person write down their social Security number. then have them rewrite it sol that it is all scrambled up. ( If they do n’t have a Social Security number, have them write down any 9 digits between 1 and 9. ) If there are any zeroes, have them change them to any other issue between 1 and 9. then have them copy their nine numbers, in the same order, right adjacent to the orginal nine numbers. This will give them a issue with 18 digits in it, with the first gear half the lapp as the second half. future change the irregular finger to a 7, and change the eleventh digit ( this will be the same number as the second digit but in the second nine digits ) to a 7 besides. then bet them that you can tell them what is left after dividing the number by 7 faster than they can figure it out by hand. The solution is 0 — 7 divides into this raw number precisely with nothing left over !

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## Fun Number Tables

The follow playfulness tables are from one of my favorite books of all clock time, Recreations in the Theory of Numbers, by Albert H. Beiler, published by Dover Publications. This book actually explains the numerical reasons these tricks work .

3 x 37 = 111 and 1 + 1 + 1 = 3

6 x 37 = 222 and 2 + 2 + 2 = 6

9 x 37 = 333 and 3 + 3 + 3 = 9

12 x 37 = 444 and 4 + 4 + 4 = 12

15 x 37 = 555 and 5 + 5 + 5 = 15

18 x 37 = 666 and 6 + 6 + 6 = 18

21 x 37 = 777 and 7 + 7 + 7 = 21

24 x 37 = 888 and 8 + 8 + 8 = 24

27 x 37 = 999 and 9 + 9 + 9 = 27

1 x 1 = 1

11 x 11 = 121

111 x 111 = 12321

1111 x 1111 = 1234321

11111 x 11111 = 123454321

111111 x 111111 = 12345654321

1111111 x 1111111 = 1234567654321

11111111 x 11111111 = 123456787654321

111111111 x 111111111=12345678987654321

1 x 9 + 2 = 11

12 x 9 + 3 = 111

123 x 9 + 4 = 1111

1234 x 9 + 5 = 11111

12345 x 9 + 6 = 111111

123456 x 9 + 7 = 1111111

1234567 x 9 + 8 = 11111111

12345678 x 9 + 9 = 111111111

123456789 x 9 +10 = 1111111111

9 x 9 + 7 = 88

98 x 9 + 6 = 888

987 x 9 + 5 = 8888

9876 x 9 + 4 = 88888

98765 x 9 + 3 = 888888

987654 x 9 + 2 = 8888888

9876543 x 9 + 1 = 88888888

98765432 x 9 + 0 = 888888888

1 x 8 + 1 = 9

12 x 8 + 2 = 98

123 x 8 + 3 = 987

1234 x 8 + 4 = 9876

12345 x 8 + 5 = 98765

123456 x 8 + 6 = 987654

1234567 x 8 + 7 = 9876543

12345678 x 8 + 8 = 98765432

123456789 x 8 + 9 = 987654321

7 x 7 = 49

67 x 67 = 4489

667 x 667 = 444889

6667 x 6667 = 44448889

66667 x 66667 = 4444488889

666667 x 666667 = 444444888889

6666667 x 6666667 = 44444448888889

etc.

4 x 4 = 16

34 x 34 = 1156

334 x 334 = 111556

3334 x 3334 = 11115556

33334 x 33334 = 1111155556

etc.

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## Did You Know…?

Each and every 2-digit issue that ends with a 9 is the summarize of the multiple of the two digits plus the sum of the 2 digits. thus, for example, 29= ( 2 X 9 ) + ( 2 + 9 ). 2 x 9 = 18. 2 + 9 = 11. 18 + 11 = 29 .

40 is a unique number because when written as “ forty ” it is the only number whose letters are in alphabetic order .

A **prime** count is an integer greater than 1 that can not be divided evenly by any other integer but itself ( and 1 ). 2, 3, 5, 7, 11, 13, and 17 are examples of prime numbers .

139 and 149 are the first base back-to-back primes differing by 10 .

69 is the lone number whose public square and cube between them use all of the digits 0 to 9 once each :

692 = 4761 and 693 = 328,509 .

One pound of iron contains an estimated 4,891,500,000,000,000,000,000,000 atoms .

There are some 318,979,564,000 possible ways of playing the first four moves on each slope in a game of chess .

The earth travels over one and a one-half million miles every day .

There are 2,500,000 rivets in the Eiffel Tower .

If all of the blood vessels in the human consistency were lay end to end, they would stretch for 100,000 miles .

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## A Math Trick for This Year

This one will purportedly only work in 1998, but actually one change will let it work for any year .

1. Pick the number of days a workweek that you would like to go out ( 1-7 ) .

2. Multiply this number by 2 .

3. Add 5 .

4. Multiply the new total by 50 .

5. In 1998, if you have already had your birthday this year, add 1748. If not, add 1747. In 1999, just add 1 to these two numbers ( therefore add 1749 if you already had your birthday, and add 1748 if you have n’t ). In 2000, the number change to 1749 and 1748. And sol on .

6. Subtract the four digit year that you were born ( 19XX ) .

Results :

You should have a three-digit numeral .

The first digit of this phone number was the number of days you want to go out each week ( 1-7 ) .

The last two digits are your historic period .

( Thanks for passing this one on to me, Judy. )

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## Where is the String?

The following meter you are with a group of people, and you want to impress them with your psychic powers, try this. Number everyone in the group from 1 to however many there are. Get a man of string, and tell them to tie it on person ‘s finger while you leave the room or turn your back. then say you can tell them not alone who has it, but which hand and which finger it is on, if they will merely do some easy mathematics for you and tell you the answers. then ask one of them to answer the watch questions :

1. Multiply the count of the person with the string by 2 .

2. Add 3 .

3. Multiply the resultant role by 5 .

4. If the string is on the right hand add 8 .

If the string is on the exit hand add 9 .

5. multiply by 10 .

6. Add the number of the finger ( the ovolo = 1 ) .

7. Add 2 .

Ask them to tell you the answer. then mentally subtract 222. The remainder gives the answer, beginning with the right finger of the answer .

For case, suppose the bowed stringed instrument is on the third base finger of the leave bridge player of Player # 6 :

1. multiply by 2 = 12 .

2. Add 3 = 15 .

3. Multiply by 5 = 75 .

4. Since the string is on the left hand, add 9 = 84 .

5. reproduce by 10 = 840 .

6. Add the number of the finger ( 3 ) = 843 .

7. Add 2 = 845 .

now mentally subtract 222 = 623. The right finger ( 3 ) tells you the string is on the third finger. The center digit tells it is on the leave hand ( the right hand would = 1 ). The left finger tells you it is Player # 6 who has the string .

By the way, when the number of the person is over 9, you will get a FOUR-digit number, and the TWO left-hand digits will be the number of the Player.

What is the Secret ?

( This is from a bang-up book called, Giant Book of Puzzles & Games, by Sheila Anne Barry. Published by Sterling Publishing Co., Inc., NY, 1978, recently reissued in paperback. )

Stay tuned for more mathematics Tricks. They will be added from prison term to time, so be certain to check in again .

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