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30Jan/106

Cyclic Number

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There is a very interesting concept called Cyclic Number.

Cyclic Numbers can be defined as a number with n digits, which, when multiplied by 1, 2, 3, ..., n produces the same digits in a different order.

There are few very famous cyclic numbers. We have given a puzzle question below, if you could answer the puzzle your concept of cyclic number will be crystal clear. That's the reason we have not given example for cyclic numbers.

Can you find a number which added to itself one or several times will give a total having the same digits as that number but differently and after the sixth addition will give a total of all nines?

Leave your answers below. We will provide the answer if you ask for :)

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Filed under: Mathematics Gyan, Puzzles Leave a comment
Comments (6) Trackbacks (0)
  1. SmiluThomas
    August 24th, 2010 - 19:49

    Take the number 142857 and multiply it by any number from 2 to 6. The result always has the same digits in the same order, if we say the first digit comes after the last.

    For instance, we have 142857 * 2 = 285714. Note that in this number, just like in 142857, the digit 1 is followed by 4, which is followed by 2, which is followed by 8, which is followed by 5, which is followed by 7, which is followed again by 1. Such an arrangement of digits is called a cyclic permutation. For this reason, the number 142857 is called a cyclic number.

    The other products, with the same property, are
    3 * 142857 = 428571,
    4 * 142857 = 571428,
    5 * 142857 = 714285, and
    6 * 142857 = 857142.

    What about 7 * 142857? If you perform this multiplication, you’ll get another surprise, namely 142857 * 7 = 999999!

    ( REPLY )
  2. khushboo
    March 28th, 2010 - 19:55

    hey how did you get this number>??? :)

    ( REPLY )
  4. Mohit
    January 31st, 2010 - 17:44

    Correct

    (142857)n

    ( REPLY )

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