post written by: Marc Chernoff

3 Fun Math Tricks


Here are 3 fun math tricks you can use to impress your geeky friends.  All three tricks are based around the sequential manipulation of the numbers being used for input and output.  One of my old college professors showed me these tricks a few years back.  I thought it was pretty cool, so I figured I’d share it.  Enjoy yourselves!

1 Through 9 to 9 Through 1:

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

Sequential Input to All 1’s:

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

All 1’s to a Numeric Palindrome:

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

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12 Comments

  • There’s also that old trick (notice there’s no “8″):

    12345679 X 9 = 111111111
    so
    12345679 X 18 = 222222222
    12345679 X 27 = 333333333

  • Don’t forget that 643×192=123456
    or that 1/8.1=.1234567

  • and that 2/3=.666
    (someone ever heard of the 23 enigma????)

  • even better, Shiny Freak is :
    2^2 +3^2+5^2 +7^2 +11^2 +13^2+17^2=666

    Uparrow means to the power of.

    Note that (not counting 1, which today is considered a prime) this is the sum of the squares of the first seven
    primes.

    Without a telescope, there were seven planets:
    back in the day that was: Sun, Moon, Mercury,
    Venus, Mars, Jupiter and Saturn.

    Which is to say: The true origin of the mystic number 666 is in the numerology cult of Pythagorus,
    which predates the Christian Bible.

    It is not in greek gematria. And has nothing to do with beasts or devils or antichrists.

    p.s. two thirds is NOT = .666
    It equals .6666…..

  • Based on the same ideas: Someone hits all fives on their
    ( say ten place) calculator, and you tell them the square root of that number with many correct
    significant figures before they can punch the square root key.

    To approximate the square root of 5555555555, you can note that 1/9= .111111111…. and thus 5/9=
    .555555555…..

    Thus, up to small error and a shift of the decimal point
    we know that the square root in question is equal
    to one third of the square roof of 5.

    Now, by standard elementary school methods, or by using a memorized log table, or by imagining a slide rule, you know the square root of five to a bunch of decimal places.

    Thus, you can quite a few places in your head, quite quickly.

    Used to do this sort of thing for entertainment when I was a child.

    p.s.

    When you use a slide rule a lot, it becomes pretty easy to see one in your head. And if you took
    trig before calculators, there was a lot of solving triangles using nasty arithmetic ( law of sines, tangents etc.) that was done with log tables. After a few weeks, you basically knew the log table (to three
    places) by heart, and simple interpolation ( which you did constantly) gave you four places. Or, you could notice that the five place log table was easy to memorize ( though large) by starting with a memorized three place log table.

    So, you could do slide rule type stuff in your head.

    The absolutely best book on mental calculation
    , in a class of its own, is titled ” Dead Reckoning”.

  • wonderful examples I will use this shortcut

  • Squaring n-digit numbers that end in 5 –>

    If a number ends in 5 then its square always ends in 25. To get the rest of the product take the left digit and multiply it by one more than itself.

    35×35 ends in 25. We get the rest of the product by multiplying 3 by one more than 3. So, 3×4 = 12 and that’s the rest of the product. Thus, 35×35 = 1225.

    To calculate 535×535, notice that 53×54 = 2862 and write down 286225 as the answer.

  • I’m really thankful 2 u . I enjoyed this a lot it all. Now i can use these tricks for my students as mind refreshers.

  • Here’s a calculator or keypad trick for you.

    456+654=1110
    258+852=1110
    159+951=1110
    753+357=1110
    741+369=1110
    147+963=1110
    789+321=1110
    987+123=1110

  • There was a 13 year old girl with breast size 84, she wanted a size 45 so she went to the doctor whom told her o take 2x of these pills every day, but instead she took 4, and she ended up (turn the calculator upside down)

    13844502×4

  • Here’s a whole bunch of such identities - with proofs, too:

    http://www.cut-the-knot.org/arithmetic/NumberCuriosities/MoreSquares.shtml

  • This is a very interesting thing to know about math. Here is another one:

    12345679*9=111111111
    41152263*3=123456789
    13717421*9=123456789

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