Another math trick

Discussion in 'Math' started by Mark44, Mar 29, 2008.

  1. Mark44

    Thread Starter Well-Known Member

    Nov 26, 2007
    626
    1
    This one requires a willing participant with a calculator...

    1. Ask the willing participant to think of a three-digit number, and to commit it to memory or write it down so that you can't see it.
    2. Ask your friend to key in the digits of the number, and then key them in again, forming a six-digit number. For example, if the first number was 283, the number keyed in should be 283283.
    3. Ask your friend to divide the number in the previous step by 13. Surprisingly, the result is an integer.
    4. Now ask your friend to divide the number in the previous step by 11. Again, the result is an integer.
    5. Finally, ask your friend to divide the number in the previous step by 7.
    6. Tell your friend that this is the same number he/she started with.

    Can someone come up with an explanation of how this works?
     
  2. Dave

    Retired Moderator

    Nov 17, 2003
    6,960
    144
    Fantastic! I really like this one! :D

    If someone hasn't already solved this by tomorrow I will sit down and have a go at working it out. We have friends round later so might crack the calculator out along side a bottle of wine!

    Dave
     
  3. Dave

    Retired Moderator

    Nov 17, 2003
    6,960
    144
    Got it with a bit of algebra!!

    I won't ruin it for others though...

    Dave
     
  4. hgmjr

    Moderator

    Jan 28, 2005
    9,030
    214
    Dave,

    I too have detemined the underpinning algebra that makes this work. It was fairly transparent.

    hgmjr
     
  5. thingmaker3

    Retired Moderator

    May 16, 2005
    5,072
    6
    The answer becomes obvious when one simplifies the division.
     
  6. mrmeval

    Distinguished Member

    Jun 30, 2006
    833
    2
    Try two digits but divide by 101. ;)
     
  7. hgmjr

    Moderator

    Jan 28, 2005
    9,030
    214
    Or try 4 digits and divide by 10001.

    Example number: 12341234

    The result would be 1234

    hgmjr
     
  8. Mark44

    Thread Starter Well-Known Member

    Nov 26, 2007
    626
    1
    Yes, that will work, but will seem more transparent to the trickee. Part of the mystery of the original version is the apparent disconnect between the 1001 multiplier and its factors--7, 11, and 13.
     
  9. Dave

    Retired Moderator

    Nov 17, 2003
    6,960
    144
    I tried this trick on my missus and she wasn't impressed, so I then tried to explain it and she became even less impressed!

    It must be bloke thing!

    Dave
     
  10. Mark44

    Thread Starter Well-Known Member

    Nov 26, 2007
    626
    1
    My wife is like that, too. She's definitely a "people" person, and has zero curiosity about "math" things, a category into which she lumps chemistry, physics, biology, computer programming, and of course math (or maths, as you would say).

    Her lack of appreciation in this area is partly due, I think, to her experience in high school geometry. The teacher was a very uninspiring guy with no sense of humor and a generally sour demeanor. After an experience like that, a lot of people just give up, and in essence wall off large sections of human thought.
     
  11. Dave

    Retired Moderator

    Nov 17, 2003
    6,960
    144
    It is a curiosity why we consider it a plural (Maths) you guys consider it a singular (Math)!! Funilly enough if we call it "Math" over hear it just sounds wrong. My web browser spell-checker pulls up Math but not Maths! :p

    Yes, its a common issue for such an important subject. My missus wasn't taught by a bad teacher, and she really liked Maths, but as a nurse she feels there is probably more to like than the geekery that we crave so much here.

    Oh well!

    Dave
     
  12. 240Volts

    New Member

    Apr 30, 2008
    1
    0
    wow thats a cool trick
     
  13. wiltec

    New Member

    May 12, 2008
    3
    0
    YOUR NUMBER CAN BE REPESENTED BY xyzxyz WHICH REALLY IS : 100000x + 10000y + 1000z +100x + 10y + z, which is: 100100x + 10010y + 1001z, which is:
    1001 x (100x + 10y + z). 1001 = 13 x 11 x 7 and 100x + 10y + z is really the number xyz.
     
  14. triggernum5

    Active Member

    May 4, 2008
    216
    0
    What factors would be good to make it work with 8008, 80085, or 80084, or even 8008135?:) I love a good math trick that works with those..
     
  15. K8MHZ

    New Member

    Jun 1, 2008
    6
    0
    Here is a fun one for all of you!

    http://www.milaadesign.com/wizardy.html

    This is my first post here. I hope you like it. This seems to be a great forum. I am also a senior member of Mike Holt's Forum and a long time member of QRZ. Forums are great ways to learn and network.

    Cheers and 73

    Mark aka Marky the Sparky
     
  16. thingmaker3

    Retired Moderator

    May 16, 2005
    5,072
    6
    Welcome to AAC, Marky!

    The first part of the "mind-reading trick" in this is a limited number of numbers. IE f(11)=9, but f(13) also = 9. The solution for f(x) where x is a 2 digit number are limited to 9, 18, 27, 36, 45, 54, 63, 72, and 81. Specifically, f(x) = 9 * INT(x/10)

    Second part of the trick is to assign a random zodiacal sign to the numbers. Same sign gets assigned to all multiples of 9. Other signs get put on non-solution numbers.
     
  17. K8MHZ

    New Member

    Jun 1, 2008
    6
    0
    Thanks for the welcome!

    Yep, you got it! It's still a cool trick for the masses. My sister sent it to me and was totally freaked out by it.

    As for astrology, I used to put astrology and weather forecasting into the same group....until I realized that astrology has some basis in scientific fact. (I live near Lake Michigan, the hardest place to forecast the weather in the country)

    Again, thanks for the welcome. This seems like a great forum!
     
  18. circuitashes

    Active Member

    May 13, 2008
    37
    0
    I realised this also. Great work. This explains why the ff are true:
    (1001*(100x + 10y + z))/13 = (100x + 10y + z)*11*7 = an integer
    ((1001*(100x + 10y + z))/13)/11 = (100x + 10y + z)*7 = an integer
    (((1001*(100x + 10y + z))/13)/11)/7 = 100x + 10y + z = xyz,
    for all x,y,z

    This completely explains the trick.
     
  19. ahrjay007

    New Member

    Jul 9, 2008
    3
    0
    i lyk that trick...awesome
     
  20. DrMarten

    New Member

    Aug 11, 2008
    5
    0

    Hi,

    I will have to check this with a computer program in Visual Basic.Net ( VB.Net )

    It seems that as 13 times 11 times 7 is 1001

    so maybe all numbers of the form XYZXYZ like 123123 are divisible by 1001

    If that is TRUE that is the reason it works.

    I'm off to test it now!!




    Regards,

    DrM.
     
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