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New Brain Teaser – What is that number?

There is a number less than 3000 that when divided by 2 leaves a
remainder of  1, when divided by 3 leaves a remainder of 2, when
divided by 4 leaves a remainder of 3, When divided by 5 leaves a
remainder of 4, when divided by 6 leaves a remainder of 5, and so on up to nine.

What is that number?

Posted by on May 2nd, 2012 and filed under Articles, Discussions. You can follow any responses to this entry through the RSS 2.0. You can skip to the end and leave a response. Pinging is currently not allowed.

3 Responses for “New Brain Teaser – What is that number?”

  1. aditya says:

    its l.c.m of (2, 3, 4, 5, 6, 7,8 ,9)k – 1
    i found l.c.m = 2520
    and k may be any natural no.
    and reason for subtracting 1 is that is the common difference between every divisor and its corresponding remainder.
    so the ans may be 2519 , 5039 and so on
    but its given the no. should be less than 3000
    so the final answer is 2519.

    its very easy.

  2. Piramyd says:

    2519. This is how it’s done:

    2=2
    3=3
    4=2×2
    5=5
    6=2×3
    7=7
    8=2x2x2
    9=3×3

    number=2x3x2(we already have a 2 for 4)x5x7(we skiped 6, because the number is a multiple of 6 already)x2x3 – 1.
    why -1?
    because for 2, the smallest number is 2×2-1, for 3 is 3×2-1, for 4 is 4×2-1, and so on.
    the condition is that our number is more than, or equals 10×2-1, and it does.

  3. Ralph H. McBride says:

    The number is 2519. Found on a TI 84+, using sequence command in the stat are of the calculator.

    Great brain teaser!

    R

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