Just How Good Are You At Maths?

“Fight Against Stupidity And Bureaucracy”

Just how good are you at maths?

I’m not talking about algebra, or trigonometry, or calculus, or anything complicated. I’m just talking about simple addition, subtraction and multiplication.


For example,

1  +  1  =  2  so far so good.

6  +  4  =  10  okay

6  +  5  =  11  yes

64  +  65  =  129  right


Let’s try some simple multiplication, for example,

8  times  8  =  64  yes, correct

5  times  13  =  65  yes, also correct

8 x 8 = 64  and 5 x 13 = 65


(8  x  8)  =  (5  x  13)   or    64  –  65  =  0    or    64  =  65

WHAT!!!  No that’s wrong, 64 cannot equal 65.


Really?  So how does this work then?

(if this graphic does not load on this page just click on it and it will open in a new page, then when you have viewed it click the back arrow to return to this page)




And while you are at it, please explain where the hole comes from in this


where does the hole come from?




Fourteen Magic Number Tricks

“Fight Against Stupidity And Bureaucracy”


In previous posts we have had ‘Beautiful Numbers’, ‘Big Numbers’, ‘Unusual Numbers’ and lots of what I called ‘Significant Numbers’.

Today, for a bit of a change, it is the turn of ‘Magic Numbers’, or magic number tricks.

I call them magic numbers because the results of some of them are predictable and on occasions magicians have incorporated them into their magic routines, where, for example, they need their ‘stooge’ to pick a certain card or a certain page in a book and want to give the audience the illusion of a random choice.

Try some of these out. Use them to do a bit of magic yourselves, or to win friends and influence people. Or just to entertain people you like or bore people you don’t like, whichever you think is appropriate.

Anyway I hope you enjoy this selection. You’ll need a calculator if you want to check  them out. 


the magic numbers


First Magic Number Trick.

Step 1:  Pick a number,

Step 2:  add 2,

Step 3:  multiply by 3,

Step 4:  subtract 6,

Step 5:  divide by 3.


You should get the number you started with.

This works for other, larger numbers. This example started with add 2 and multiply 3. But any two numbers work, just multiply them together to get the next number that you subtract.



Second Magic Number Trick.

Step 1:  Pick a number,

Step 2:  square it (probably need a calculator for big numbers),

Step 3:  add twice the original number,

Step 4:  add one,

Step 5:  take the square root (rounding it to the nearest whole number, 7.999… becomes 8),

Step 6:  subtract 1,


You should get the number you started with.


Third Magic Number Trick.  

Step 1:  Pick a number,

Step 2:  square it,

Step 3:  add ten times the original number,

Step 4:  add 25,

Step 5:  take the square root (rounding to the nearest whole number),

Step 6:  subtract your original number.


The answer should always be 5.


Third Magic Number Trick.

Here is a slightly more complicated one.

Step 1:  Pick a number between 1 and 100,

Step 2:  add 28,

Step 3:  multiply by 6,

Step 4:  subtract 3,

Step 5:  divide by 3,

Step 6:  subtract the original number plus 3,

Step 7:  add 8,

Step 8:  subtract the original number minus 1,

Step 9:  multiply by 7.


Your answer should be 427.


Fourth Magic Number Trick.

Step 1:  Pick a number 1 through 9,

Step 2:  multiply by 12345679 (notice there is no 8 there),

Step 3:  multiply by 9.


Do you see your original number?


Fifth Magic Number Trick.

Step 1:  Pick a 3-digit number in which the first and last digits differ by more than one,

Step 2:  reverse this number (for example, 531 becomes 135) and subtract the smaller from the larger,

Step 3:  add this number to the reverse of itself.


Your answer is 1089.


Sixth Magic Number Trick.

Step 1: Think of a 3 digit number.

Step 2: Multiply it by 7, then by 11, and then by 13.


Your answer should be your original number twice,

for example, if you chose the number 456, your answer would be 456456


Seventh Magic Number Trick.   

Step 1: Think of a 2 digit number.

Step 2: Multiply it by 3, then by 7, then by 13, and then by 37.


You should see your original number repeated three times.

For example, if your number was 45, the answer would be 454545


Eighth Magic Number Trick.  

Step 1: Think of a 5 digit number.

Step 2: Multiply it by 11.

Step 3: Multiply it by 9091.


For example, if the number is 12345, the answer should be 1234512345


Ninth Magic Number Trick.

If you multiply 1089 by 9 you get 9801. The number has reversed itself!

This also works with 10989 or 109989 or 1099989 and so on.



Tenth Magic Number Trick.

19 = 1 x 9 + 1 + 9 and 29 = 2 x 9 + 2 + 9.

This also works for 39, 49, 59, 69, 79, 89 and 99.


Eleventh Magic Number Trick.

2 is the only number that gives the same result added to itself as it does times by itself.

In other words  2 + 2  =  4  =  2 x 2,  or,   (2+2) – (2 x 2) = 0 


Twelfth Magic Number Trick.

If you multiply 21978 by 4 it turns backwards


Thirteenth Magic Number Trick.

153, 370, 371 and 407 are all the sum of the cubes of their digits.

In other words 153 = 13+53+33,  370 = 33+73+03,  371 = 33+73+13,  153 = 43+03+73,    


Fourteenth Magic Number Trick.

1 divided by 37 = 0•027027027


1 divided by 27 = 0•037037037





Significant Number Factoid Friday – Thirteen, Unlucky For Some

“Fight Against Stupidity And Bureaucracy”


They’ve been ‘beautiful’,  they’ve been ‘big’  and they’ve been ‘unusual’

Today we have ‘significant’ number thirteen, unlucky for some.



13 Thirteen

The number 13 seems to give a lot of people trouble. Indeed the fear of the number 13 is so pervasive that it even has a phobia named after it  –  triskaidekaphobia. 


In the Bible.

  • At the Last Supper in Christian theology, there were 13 dinner guests, so that number is unlucky because Christ was betrayed.
  • Thirteen famines are recorded in the Scriptures.
  • The destruction of Jericho is stamped with the number thirteen, because the city was compassed once each day for six days, and seven times on the seventh day, making 13 times in all (6+7).
  • All the names of Satan are divisible by thirteen.
  • In Mark 7 Jesus mentions thirteen things that defile a person (evil thoughts, adulteries, fornications, murders, thefts, covetousness, wickedness, deceit, lewdness, an evil eye, blasphemy, pride and foolishness).



  • The ancient Hebrews thought 13 was unlucky because the thirteenth letter of the Hebrew alphabet is the letter M, which is the first letter in the word “mavet,” meaning death.
  • In Norse mythology, 12 benevolent gods were gathering in a hall and the evil god Loki attacked the group. Loki was the 13th guest, and the god Balder was killed in the melee.
  • President Franklin D. Roosevelt was quite fearful of the number 13, and he took great pains to avoid hosting a meal for a group of that size. It is said that if he had a cancellation and it looked as if there might be 13 people to lunch, he would invite his secretary to join them so there wouldn’t be 13.
  • Industrialist Henry Ford wouldn’t do business on Friday, the 13th.
  • Multimillionaire Paul Getty once stated “I wouldn’t care to be one of thirteen at a table.”
  • Some speculate that a fear of the number 13 is the reason we recognize only 12 constellations in the Zodiac, omitting a thirteenth… Ophiuchus ( the Serpent Holder) that, by its location, could be included.
  • Years ago, London bakers were subject to harsh penalties if they were caught selling bread in what was called short weight. The bakers would add an extra loaf to each dozen to be sure the sale met the minimum weight requirement. They avoided the word thirteen and the process of adding an extra loaf became known as the “baker’s dozen.”
  • Some airlines do not have a 13th row.
  • Most tall buildings do not have a 13th floor.
  • Many hotel guests refuse to stay in Room 13, so rooms are frequently numbered 12, 12A, and 14.
  • The 13th card of the Tarot is the card of Death.
  • The composer, Arnold Schoenberg, was a noted triskaidekaphobe. He died as he had predicted at the age of 76 (7+6=13), on a Friday 13th at 13 minutes to midnight.
  • In April 1970, NASA launched Apollo 13 at 1313 hours Central Time from pad 39. The flight was commanded by James A. Lovell with John L. “Jack” Swigert as Command Module pilot and Fred W. Haise as Lunar Module pilot. (Swigert was a late replacement for the original CM pilot Ken Mattingly, who was grounded by the flight surgeon after exposure to German measles.) They were scheduled for rest periods beginning 13 minutes past the hour and on April 13 at 21:07:53 CST (55:54:53 Ground Elapsed Time) an oxygen tank exploded and the mission had to be aborted. The rest is history – and a movie, Apollo 13, based on ‘Lost Moon’, Jim Lovell’s and Jeffrey Kluger’s book about the event.
Apollo 13 insignia
Insignia of the ill-fated Apollo XIII Mission


Friday the 13th Myths:

  • If you cut your hair on Friday the 13th, someone in your family will die.
  • A child born on Friday the 13th will be unlucky for life.
  • If a funeral procession passes you on Friday the 13th, you will be the next to die.


In the United States

  • the Thirteenth Amendment to the Constitution officially outlaws slavery and involuntary servitude, except as punishment for a crime.
  • thirteen colonies rebelled against British Rule and King George III in what led to the American Revolutionary War and the eventual birth of the United States of America. The colonies were Delaware, Pennsylvania, New Jersey, Georgia, Connecticut, Massachusetts Bay, Maryland, South Carolina, New Hampshire, Virginia, New York, North Carolina, and Rhode Island and Providence Plantations.
  • there are thirteen stripes on the USA flag to commemorate these original colonies.
USA flag - Stars and Stripes
USA flag – Stars and Stripes





Significant Number Factoid Friday – Seven

“Fight Against Stupidity And Bureaucracy”


They’ve been ‘beautiful’, they’ve been ‘big’ and they’ve been ‘unusual’. Today we have the number seven, another of what are known as ‘significant’ numbers, so-called because of their use and the beliefs surrounding them.



7 Seven

The number seven is the most mystical of all numbers. It is considered by a great many people to be ‘lucky’.

It is a number that is mentioned many times in the Bible where it indicates perfection and has its roots in ancient Jewish history.

In the Old Testament for example,

  • The Creation established the pattern of a seven day week.
  • The seventh day was a day of rest.
  • Land was to lie fallow every seventh year to allow it to recover its nutrients.
  • Noah led the clean animals into the ark in sets of seven pairs for each species.
  • Solomon took seven years to build the temple in Jerusalem.
  • The Torah mentions that the Sabbatical, or holy year, occurred every seven years.
  • The Israelites were told to march around the walls of Jericho seven times, and their enemies would be defeated.
  • The symbolic Jewish candlestick has seven branches.

This view of the number seven continued in the New Testament.

  • A disciple asked Jesus, “How many times should we forgive our brethren?” Jesus replied, “70 times 7”.
  • Revelations 1:16 states, “He had in his right hand seven stars.”
  • Also in Revelations, the number of seals is seven.


And beyond the Bible, we find the number seven in other religions and societies.

  • The ancient Greeks considered the number seven to be lucky. They believed it to be the perfect number.
  • In ancient Egypt there were seven paths to heaven.
  • In ancient Babylon there were seven branches on their tree of life.
  • The Arabs carried on this belief and built seven holy temples.
  • The Goths made sure they worshiped the seven deities.
  • The Japanese also had seven gods. (In 1995, to celebrate the Japanese Emperor’s seven year reign 17 runners ran 7,777 meters round the imperial palace at 7 minutes past seven on the 7th day of the 7th month.)
  • The Chinese saw seven as the number governing female life.
  • Even the Scottish Masons made sure the number seven had relevance in their rites, and their aprons were made with seven tassels on them.


In the US too there are examples of the occurrence of the number seven.

  • The Founding Fathers declared independence from Britain during the seventh month.
  • There are seven articles to the US constitution.
  • And the city of Washington D.C. was built on the 77th longitude.


The number still occurs because of it being thought lucky such as the drink 7-Up and the Boeing airplanes which are always 7?7.


Then there are the Seven Wonders of the world.

The original seven wonders were:

  • Great Pyramid of Giza
  • Hanging Gardens of Babylon
  • Statue of Zeus at Olympia
  • Temple of Artemis at Ephesus
  • Mausoleum at Halicarnassus
  • Colossus of Rhodes
  • Lighthouse of Alexandria

(The earliest lists had the Ishtar Gate as the seventh wonder of the world instead of the Lighthouse of Alexandria.)

Map of the original Seven Wonders of the World
Map of the original Seven Wonders of the World

In 2001 an initiative was started by the Swiss corporation New7Wonders Foundation to choose the New7Wonders of the World from a selection of 200 existing monuments.

Twenty-one finalists were announced January 1, 2006. Egyptians were not happy that the only surviving original wonder, the Great Pyramid of Giza, would have to compete with the likes of the Statue of Liberty, the Sydney Opera House, and other landmarks, calling the project absurd. In response, Giza was named an honorary Candidate.

The results, announced on July 7, 2007, in Lisbon, Portugal, were: 

  • Great Wall of China
  • Petra (Jordan)
  • Christ the Redeemer (Brazil)
  • Machu Picchu (Peru)
  • Chichen Itza (Mexico)
  • Colosseum (Italy)
  • Taj Mahal (India)


There have also been several atempts to compile a list of the Seven Natural Wonders of the World. The main candidates include:

  • Grand Canyon
  • Great Barrier Reef
  • Harbor of Rio de Janeiro
  • Mount Everest
  • Aurora
  • Parícutin volcano
  • Victoria Falls


And, of course, in the field of entertainment the number seven has featured in several memorable movies, examples of which include:

  • Snow White and the Seven Dwarfs
  • Seven Brides for Seven Brothers
  • Se7en
  • The Magnificent Seven
  • The Seven Samurai
  • The Seventh Seal
  • Seven Pounds


Factoid Friday – Significant Numbers: Is Three A Crowd?

“Fight Against Stupidity And Bureaucracy”


In the past on this blog they’ve been ‘beautiful’, they’ve been ‘big’ and they’ve been ‘unusual’. Today we have the first of a selection of ‘significant’ numbers, so-called because of their use and the beliefs surrounding them.



3 Three

The number 3 is perhaps the most significant of all numbers. I’m sure at some time in our lives we have all heard that “things happen in 3’s.” There are lots of sayings and superstitions connected with the number 3. For example,

  • luck, especially bad luck, is often said to “come in threes”;
  • there is an American superstition which says that celebrity deaths tend to occur in threes;
  • in Vietnam, there is a superstition that considers it bad luck to take a photo with three people in it; it is professed that the person in the middle will die soon;
  • some people believe that it is unlucky to take a third light, that is, to be the third person to light a cigarette from the same match or lighter. (This superstition is said to have originated among soldiers in the trenches of the First World War when a sniper might see the first light, take aim on the second and fire on the third.);
  • the phrase “Third time’s the charm” is the opposite of the previous belief and refers to the superstition that after two failures in any endeavor, a third attempt is more likely to succeed; although where something illegal is involved it can mean that the third man to do something gets caught.


Many world religions contain triple deities or concepts of trinity, including,

  • the Christian Holy Trinity (Father, Son and Holy Spirit);
  • the Hindu Tridevi and Trimurti (Brahma the Creator, Vishnu the Preserver, and Shiva the Destroyer );
  • the Three Jewels of Buddhism;
  • the Three Pure Ones of Taoism (heaven, human, earth);
  • and the Triple Goddess of Wicca.

There are also three main Abrahamic religions: Christianity, Islam, and Judaism.


According to the Chinese, 3 is a perfect number.

To the Mayan, the sacred number of woman.

Egyptians see it as the number of the cosmos.


There are three types of universe  –  matter, astral (mental or soul) and spirit.

There are three main galaxy morphological classifications: Ellipticals, Spirals and Lenticulars.

The Roman numeral III stands for giant star in the Yerkes spectral classification scheme.

Earth is the third planet in its local Solar System, hence the name of the popular comedy show ‘3rd Rock From The Sun’.

The Moon has three phases.


Three is the atomic number of lithium.

Atoms consist of three constituents  –  protons, neutrons, and electrons.

There are three types of matter  –  animal, vegetable, and mineral.


There are 3 primary colors with which it is possible to obtain all the other colors we can see, because human color vision is trichromatic (because the brain uses three independent channels to process color information).

Strangely though, different applications use a different combination of primary colors, for example, CRT (TV) displays which use additive combinations of colors, normally have red, green, and blue as their primary colors; whereas in printing, which uses a subtractive combination of colors, the primary colors are usually cyan, magenta, and yellow; although most artists prefer the  red, yellow, blue combination.


Finally, a natural number is divisible by three if the sum of its digits in base 10 is divisible by 3. For example, the number 21 is divisible by three (3 times 7) and the sum of its digits is 2 + 1 = 3. Because of this, the reverse of any number that is divisible by three (or indeed, any permutation of its digits) is also divisible by three. For instance, 1368 and its reverse 8631 are both divisible by three (and so are 1386, 3168, 3186, 3618, etc..).


And finally, finally, how about 3 Degrees  


Some Unusual Numerical Factoid Fun For Friday

“Fight Against Stupidity And Bureaucracy”


We’ve had ‘beautiful’ numbers and ‘big’ numbers on this blog. Today it’s time for some ‘unusual’ ones.


Did you know….



That ‘1’ is the only positive whole number that you can add to 1,000,000 and you get an answer that’s bigger than if you multiply it by 1,000,000,

i.e. 1 x 1,000,000 = 1,000,000  but  1 + 1,000,000 = 1,000,001

Go ahead try it with other whole numbers.



That there are 12,988,816 different ways to cover a chess board with 32 dominoes.



That sixty-nine squared = 692 = 4761 and sixty-nine cubed = 693 = 328509, and that these two answers use all the digits from 0 to 9 between them.



That you can chop a big lump of cheese into a maximum of 93 bits with 8 straight cuts



That in the English language ‘forty’ is the only number that has all of its letters in alphabetical order.



That 132 = 169 and if you write both numbers backwards you get 312 = 961.

This also works with 12 because 122 = 144 and 212 =441.



That 1/1089 = 0·00091827364554637281… (And the numbers in the 9 times table are 0, 9,18,27,36…..)



That the number ‘four’ is the only number in the English language that is spelt with the same number of letters as the number itself.



Beautiful Numbers

“Fight Against Stupidity And Bureaucracy”


I’ve heard it said that there are three kinds of mathematicians — those who can count and those who can’t.  

That seems to be getting more and more true. It used to be by the time we left school we all had a basic knowledge of arithmetic. Enough to count our change and balance our check books. Sadly that is no longer the case.

For most of us that was as far as mathematics went. For others it led to algebra, geometry, trigonometry, calculus and even something they called advanced maths.

But what we all missed in school, no matter whether our knowledge was basic or advanced, was the fact that numbers can sometimes be beautiful, both in what they can do and the patterns they can make.

Here are a few examples below that I hope you find at least a little bit interesting.


But first a joke. It’s a oldie and involves my old friend Dubya, who for many years provided me with an endless source of amusement. Damn I miss him for that! Anyway, here’s the joke….


President Bush’s morning security briefing is wrapping up.  

Defense Secretary Donald Rumsfeld is concluding his part and says, “Finally, three Brazilian soldiers were killed yesterday near Baghdad.”

“OH MY GOD!” shrieks Bush, and he buries his head in his hands for a seemingly interminable 30 seconds.  

Stunned at the unexpected display of emotion, the President’s staff sits speechless, not sure how to react.

Finally, Bush looks up and asks Rumsfeld, 

“How many is a brazillion?”


Now for the beautiful numbers


  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



67 x 67 = 4489

667 x 667 = 444889

6667 x 6667 = 44448889

66667 x 66667 = 4444488889

666667 x 666667 = 444444888889

6666667 x 6666667 = 44444448888889



4 x 4 = 16

34 x 34 = 1156

334 x 334 = 111556

3334 x 3334 = 11115556

33334 x 33334 = 1111155556



A Truly Remarkable Number

Enter the number 999999 into your calculator, then divide it by seven.

The result will be a mysterious number!


Throw a die (or randomly pick a number from 1 to 6) and multiply the result by the mysterious number.


Arrange the digits of the product from lowest to highest from left to right to form a six-digit number.




Intelligent Design


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.

Do it as many times as you want, selecting a different word from the first 20 each time.