Safe key decrypt puzzle

There is a safe with a 5 digit number as the key. The 4th digit is 4 greater than the second digit, while the 3rd digit is 3 less than the 2nd digit. The 1st digit is thrice the last digit. There are 3 pairs whose sum is 11.

Find the key to open the safe.

safe number key puzzle

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SherlockHolmes Expert Asked on 9th February 2016 in Math Puzzles.
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  • 2 Answer(s)
    Best answer

    let 5 digits be

    a b c d e

    now,

    eq1=>    d= 4+b,
    eq2=>    c = b- 3
    eq3=>     a =3e,

    As a,b,c,d,e are single digits can varies from 0-9

    so
    bmax <= 5 , from eq1
    bmin >= 3, from eq

    similarly
    dmax = 9
    dmin = 7

    cmax = 2
    cmin= 0

    e can be     0, 1,2,3
    a will be     0,3,6,9 respectively

    So ranges are
    0<=a<=9
    3<=b<=5
    0<=c<=2
    7<=d<=9
    0<=e<=3

    Possible pairs are
    ab, ac, ad, ae,     bc, bd, be,     cd, ce,      de

    Also there are only three pairs whose sum should be 11
    there are 9 cases lets find one by one
    a.) if b= 3 => then  c = 0, d= 7
    (i)  a = 9,  e= 3,
    or  (ii) a = 6,  e = 2,
    or (iii) a = 3, e =1

    b.) if b = 4 => then c=1, d=8
    (i)  a = 9,  e= 3,
    or  (ii) a = 6,  e = 2,
    or (iii) a = 3, e =1

    c.) if b = 5 => then c=2, d= 9
    (i)  a = 9,  e= 3,
    or  (ii) a = 6,  e = 2,
    or (iii) a = 3, e =1

    So from this only c(ii) shows the desired result
    a+b= 11, c+d =11, d+e = 11

    so answer is
    a=6,b=5,c=2,d=9,e=2

    ie. 65292

    hddev Guru Answered on 15th February 2016.
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    answer is  65292

    puzzlesmruti Curious Answered on 10th February 2016.

    How?

    on 10th February 2016.
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