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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?

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Brain Teaser: A Sliding Ladder

A 25 ft ladder (assume it is not an extension ladder) is placed with its foot 7 ft away from a building. If the top of the ladder slips down 4 ft, how many feet will the bottom slide out?


  1. 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. 2519. This is how it’s done:


    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

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

    Great brain teaser!


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