Amaze the peons with this one. It's simple. It's effective. It gets them every time.
Every row and column sums to 15 in this magic square. So do both diagonals!
Every row and column sums to 34 in this magic square. So do both diagonals!
Here's a recipe for making your own 3 X 3 magic number square. This recipe and both of the above two magic squares comes from one heck of a great book called, Mathematics for the Million, by Lancelot Hogben, published by Norton and Company. I highly recommend it. You don't need much math at all to get into the adventure of numbers told in this classic book.
Some necessary rules and definitions:
To create the first Magic Square #15 above, you let a be equal to 5, let b be equal to 3, and let c be equal to 1. Here are some others:
Try making up some of your own.
Here's a magic square that not only adds up to 264 in all directions, but it does it even when it's upside down! If you don't believe me, look at it while you are standing on your head! (Or, just copy it out and turn it upside down.)
Here's a magic square with as many different totals as possible.
This table produces 8 different totals.
OK, here's a neat way to win bets with a magic square. Call a friend on the phone. Have him or her get a pencil and paper and bring it to the phone, 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 number 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 number, and so do you. When you say a number, you draw a square around that number, and so does your friend. The winner is whoever is the first one to get three numbers that add up exactly 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 friend calls out 7, and you call out 3. Then you tell your friend that you have just won because you called out 8, 3, and 4, which add up to 15.
Your friend will want to play again. So this time you can bet him you'll win, with the condition that in case of a draw (where you use up the numbers 1 to 9 without either of you getting a 15 total) nobody 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 tic-tac-toe and a magic square. The magic square look like this:
Because this is a magic square, every row and every column and every diagonal adds up to 15. So if you've got this square in front of you with your friend on the phone, you can put an X in the squares of the number you call out, and an O in the squares of the numbers your friend calls out. Then, just like in tic-tac-toe, you try to get three X's in a row, because those will always add up to 15.
So in the example above, when you call out 8, you put an X in the upper left corner. When your friend says 6, you put an ) in the upper right corner. And so on.
You need an ordinary pack of cards for this wower. No fancy shuffling is required. Just follow these easy steps:
Here's a trick to wow them everytime! Have someone write down their Social Security number. Then have them rewrite it so that it is all scrambled up. (If they don'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 number between 1 and 9. Then have them copy their nine numbers, in the same order, right next to the orginal nine numbers. This will give them a number with 18 digits in it, with the first half the same as the second half. Next change the second digit 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 also. 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 answer is 0 -- 7 divides into this new number exactly with nothing left over!
The following fun tables are from one of my favorite books of all time, Recreations in the Theory of Numbers, by Albert H. Beiler, published by Dover Publications. This book actually explains the mathematical reasons these tricks work.
Each and every 2-digit number that ends with a 9 is the sum 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 alphabetical order.
A prime number is an integer greater than 1 that cannot 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 consecutive primes differing by 10.
69 is the only number whose 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 side in a game of chess.
The earth travels over one and a half million miles every day.
There are 2,500,000 rivets in the Eiffel Tower.
If all of the blood vessels in the human body were laid end to end, they would stretch for 100,000 miles.
This one will supposedly only work in 1998, but actually one change will let it work for any year.
1. Pick the number of days a week 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 (so add 1749 if you already had your birthday, and add 1748 if you haven't). In 2000, the number change to 1749 and 1748. And so on.
6. Subtract the four digit year that you were born (19XX).
You should have a three-digit number.
The first digit of this number was the number of days you want to go out each week (1-7).
The last two digits are your age.
(Thanks for passing this one on to me, Judy.)
The next time 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 piece of string, and tell them to tie it on someone's finger while you leave the room or turn your back. Then say you can tell them not only who has it, but which hand and which finger it is on, if they will just do some easy math for you and tell you the answers. Then ask one of them to answer the following questions:
1. Multiply the number of the person with the string by 2.
2. Add 3.
3. Multiply the result by 5.
4. If the string is on the right hand add 8.
If the string is on the left hand add 9.
5. Multiply by 10.
6. Add the number of the finger (the thumb = 1).
7. Add 2.
Ask them to tell you the answer. Then mentally subtract 222. The remainder gives the answer, beginning with the right-hand digit of the answer.
For example, suppose the string is on the third finger of the left hand 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. Multiply by 10 = 840.
6. Add the number of the finger (3) = 843.
7. Add 2 = 845.
Now mentally subtract 222 = 623. The right-hand digit (3) tells you the string is on the third finger. The middle digit tells it is on the left hand (the right hand would = 1). The left-hand digit 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 great 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 Math Tricks. They will be added from time to time, so be sure to check in again.