Secret Word

When in the Course of human Events, it becomes necessary for one People to dissolve the Political Bands which have connected them with another, and to assume, among the Powers of the Earth, the separate and equal Station to which the Laws of Nature and of Nature's God entitle them, a descent Respect to the Opinions of Mankind requires that they should declare the causes which impel them to the Separation.

Printed above is the first paragraph of the U.S. Declaration
of Independence. Select any one of the first 20 words. Count the letters and call that number n. Move ahead n words, beginning with the word after your selected word. When you reach that nth word, count its letters and move ahead as many words as the new letter count. Continue in this manner, counting letters and moving ahead words, until you stop on a word that's beyond the fourth line.
On what word did you stop? Magic created by Martin Gardner.

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Magic 8

Multiply your phone number, a seven-digit number
(no area code) by the number 8.
Then write down the following three numbers:
(i) your phone number,
(ii) the number 8,
(iii) the product of your phone number times 8.
Add up the numeric values all the individual digits in those three numbers. If the sum is more than one digit, take that sum and add up its digits. Continue adding up digits until only one digit is left.
What is that single digit? Magic created by Martin Gardner.

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Number Names

Think of any number from 1 through 100. (Say 10)
Write down its name. (ten)
Count the number of letters in its name to obtain a second number. (3 letters)
Count the number of letters in the second number to obtain a third number. (three,5 letters)
Continue in this way until the chain of numbers ends on a number that keeps repeating.
What is the final repeating number? Magic created by Martin Gardner.

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Remarkable Number

Enter 999999 into your calculator.
Divide the above number by seven.
The result will be a mysterious number!
Throw a die, or randomly pick a number from 1 to 6.
Multiply the result times the mysterious number.
Arrange the digits of the product from lowest to highest from left to right to form a six-digit number.
What is the number? Magic created by Martin Gardner.

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Magic Number

Write down any 3-digit number. (Let's say, 276)
Write it down again beside itself. (This means 276276)
Divide that result by 7. (Answer is 39468)
Divide that result by 11. (Answer is 3588)
Divide that result by 13. (Answer is 276, the original number)
Why does this happen?
Writing a 3-digit number beside itself is equivalent to multiplying it by 1001 because 1001 = 7 x 11 x 13. So, all that is being done by dividing the large number by 7, 11 and 13, is to return it to the original 3-digit number.

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Tautonymic Numbers

A Tautonymic number is one which can be broken into two equal non-palindromic halves
and with each part having at least two different digits.
Examples of tautonymic numbers are 5656, 2525, 3737, 4141, 165165, 34723472 etc..

How many bygone tautonymic years can you write down?

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Tetradic Numbers

A Tetradic Number is one which is both strobogrammatic and palindromic in nature. It is the same when viewed from left to right, right to left, top to bottom or upside down. This four-way symmetry explains the name, tetra- being the greek prefix for four.
The only digits that can be found in a tetradic number are 0, 1 and 8, since although matched pairs of 6 and 9 can be used in strobogrammatic numbers, they won't yield a palindrome. Thus the first few tetradic numbers are 0,1,8,11,88,101.
Given a tetradic number, a larger one can always be generated by adding another tetradic number to each end, retaining the symmetry. There are tetradic primes, the first half dozen being 11, 101, 181, 18181, 1008001, and 1180811.

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Strobogrammatic Numbers

A Strobogrammatic Number is a number that appears the same whether viewed normally or upside down. In base 10, given that 0, 1 and 8 are symmetrical around the horizontal axis, and 6 and 9 are the same as each other upside down, the first few strobogrammatic numbers are:
1, 8, 11, 69, 88, 96, 101,
111, 181, 609, 619, 689, 808,
818, 888, 906, 916, 986, 1001

What years are strobogrammatic?

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Kaprekar Number

The Kaprekar Number is 6174.
(1) Take any four-digit number.
(2) Form the largest and the smallest numbers from these four digits.
(3) Find the difference between those digits. Maybe this is 6174.
If it is not, form the largest and the smallest number from the difference and subtract these numbers again. You may have to repeat this procedure.
The end result is always 6174, with no more than 7 steps.

Take the number 3546.
1st step: 6543 - 3456 = 3087
2nd step: 8730 - 0378 = 8352
3rd step: 8532 - 2358 = 6174

Take the number 5184.
1st step: 8541 - 1458 = 7083
2nd step: 8730 - 0378 = 8532
3rd step: 8532 - 2358 = 6174

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Josephus Problem

The Classic Josephus Problem :
X people stand in a circle. An extra person goes round the circle eliminating every Yth person. When the start of the circle is reached, we continue going round again, ignoring the people who have already been eliminated, and still eliminating every Yth person.
The Problem : Given the values of X and Y, where should you stand in the circle so that you will be the last to be eliminated?

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Math Phrases

Common Phrases Used in Math Class -
FINALLY: Only a few more steps to go...
Q.E.D. : Quite easily done.
PROOF OMITTED: Trust me, it's true.
ONE MAY SHOW: I will leave it to you to prove this.
SIMILARLY: Most of this proof is the same as before.
CLEARLY: I don't want to write down all the in-between steps.
TWO LINE PROOF: I'll leave out everything but the conclusion.
TRIVIAL: If I have to show you this, you're in the wrong class.
OBVIOUSLY: I hope you weren't asleep, because I refuse to repeat it.
RECALL: I shouldn't really have to tell you this, but here it is again.
WITHOUT LOSS OF GENERALITY: I did one case, so now you figure out the rest.
IT IS WELL KNOWN: Don't embarrass yourself by asking any questions about this.
CHECK FOR YOURSELF: This is boring, so you can do it on your own time.
BRUTE FORCE: If you understand this overblown proof, then you are really good.
ELEGANT PROOF: Above your head, and less than six lines long.
THESE ARE EQUIVALENT: Since this shows that, and that shows this, then the other thing must also be correct.
BY A PREVIOUS THEOREM: I forgot how it goes, but I'm sure this is right.
BRIEFLY: I'm running out of time, so I'll just write and talk faster.
LET'S TALK IT THROUGH: I don't really want to write it on the board
because I might make a mistake.
PROCEED FORMALLY: Manipulate symbols randomly with confusing explanations.
QUANTIFY: I can't find anything wrong with your proof
except that it doesn't work.

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Number 8

9 x 9 + 7 = 88
9 x 98 + 6 = 888
9 x 987 + 5 = 8888
9 x 9876 + 4 = 88888
9 x 98765 + 3 = 888888
9 x 987654 + 2 = 8888888
9 x 9876543 + 1 = 88888888
9 x 98765432 + 0 = 888888888.

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Weird Numbers

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

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Curious Numbers

1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321

12345679 x 9 = 111 111 111
12345679 x 8 = 98765432

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Numerology

  Calculate Your Numerology Number
1=A,J,S 2=B,K,T 3=C,L,U
4=D,M,V 5=E,N,W 6=F,O,X
7=G,P,Y 8=H,Q,Z 9=I,R

  Personality Characteristics
1 = ambitious, independent, and self-sufficient.
2 = supportive, diplomatic, and analytical.
3 = enthusiastic, optimistic, and fun-loving.
4 = practical, traditional, and serious.
5 = adventurous, mercurial, and sensual.
6 = responsible, careful, and domestic.
7 = spiritual, eccentric, and a bit of a loner.
8 = money-oriented, decisive, and stern.
9 = multi-talented, compassionate, and global.

  To Find Your Number Add Values of Letters of Your Name
If your name is Tom, your number is 2+6+4=12 and 1+2= 3
And you are enthusiastic, optimistic, and fun-loving.
If your name is Helen, your number is 8+5+3+5+5=25 and 2+5= 7
And you are spiritual, eccentric, and a bit of a loner.

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Baking

1)Mother bought three different types of apples.
2)She made 3 items - pies, muffins and tarts.
3)She used only one type of apple in each item.
4)She added raisins, pecans, or walnuts to one item.
5)The pies did not contain any nuts.
6)Cortland apples were used in the muffins.
7)The McIntosh apples were mainly red.
8)The raisins tasted great with the McIntosh apples.
9)The walnuts were not in the muffins.
10)The tarts were made with multigrain flour.
11)The pies were not made from the Empire apples.
Which apple and which ingredient went into each item?

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