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Posted by Karl Sharman on November 12, 2010 – 8:58 am

What is the 5-digit number in which the sum of the first two digits is one smaller than the third, the third is double the fourth, the fourth is double the last, the third is the product of the fourth and fifth, the second is five more than the first, and the first is one-eighth the third and also one-fourth of the fourth?

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  1. 1. Dual Aspect Said:

    16842

    If the third is double the fourth, and the fourth is double the fifth, then there are only 2 combinations of the last 3 digits that would fit that solution (_ _ 8-4-2 or _ _ 4-2-1).

    If the third is the product of the fourth and fifth then _ _ 4-2-1 doesn’t work so the last digits are 8-4-2.

    The first is 1/8 the third and 1/4 the fourth so must be 1

    The second is five more than the first so must be 6.

    As a check we also know that the sum of the first two is one less than the third (1+6 = 8-1)

  2. 2. DP Said:

    i came up with 7 equations for 5 unknowns…

    lets say the 5-digit number is represented by ‘abcde’

    a + b = c – 1
    c = 2 * d
    d = 2 * e
    c = d * e
    b = a + 5
    a = 1/8 * c
    a = 1/4 * d

    a = 1; b = 6; c = 8; d = 4; e = 2

    16842

  3. 3. DP Said:

    Well done Dual Aspect. beat me by 1 minute.

  4. 4. Rohan Said:

    16842….

  5. 5. GODFATHER Said:

    i did it somehow but the answer was the same like all the others..16842 …but very tricky .:P

  6. 6. joann Said:

    11248

  7. 7. perixosome Said:

    16842
    i did exactly the same like DP..

  8. 8. Chris Said:

    The first 5 statements can be written as:
    (1) a + b – c = -1
    (2) c – 2d = 0
    (3) d – 2e = 0
    (4) a – b = -5
    (5) 8a – c = 0

    The sixth statement is redundant.

    (1)+(4) => (6) 2a – c = -6
    (5)-4(6) => 3c = 24 => (7) c = 8
    (7)-(2) => 2d = 8 => (8) d = 4
    (7)+(5) => (9) a = 1
    (9)-(4) => (10) b = 6
    (8)-(3) => (11) e = 2

    So abcde = 16842

  9. 9. Chris Said:

    You can solve simultaneous equations on wolframalpha:
    http://www.wolframalpha.com/input/?i=a%2Bb%2B1%3Dc%2Cc%3D2d%2Cd%3D2e%2Cb%3Da%2B5%2C8a%3Dc dow it for this problem.

  10. 10. gaurav Said:

    16842

  11. 11. Euclid's Brother Said:

    I came up with 16842. Looks like many others did too. I didn’t use any math, just followed the rules in the order that I used them:

    “The 3rd is double the 4th” and “The 4th is double the 5th”
    Possibilities:
    xx421
    xx842

    “The first 2 digits is one smaller than the 3rd”
    Possibilities:
    12421
    21421
    30421
    34842
    43842
    52842
    25842
    16842
    61842
    70842

    “The 3rd is the product of the fourth”, which knocks out the xx421 numbers.
    Possibilities:
    34842
    43842
    52842
    25842
    16842
    61842
    70842

    “The 2nd is five more than the first”. This is narrows it down to:
    16842

    “The first is one-eight the third and also one-fourth the fourth”. this just confirms that it still works with 16842.

  12. 12. John24 Said:

    16842

    Far too much information was provided.

    What is the 5-digit number in which the sum of the first two digits is one smaller than the third, the third is double the fourth, the fourth is double the last, and the first is one-eighth the third and also one-fourth of the fourth?

    These are not needed. the third is the product of the fourth and fifth, the second is five more than the first

  13. 13. Simtrac Said:

    16842

    five more than the first made this easy
    The first is one-eight the third and also one-fourth the four just confirmed it

  14. 14. Niyas Y Said:

    16842

    i did the way hw gaurav did!
    its correct 1+6=8-1
    8=4×2
    1/8×8=1 nd 1/4×4=1

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