Vault code Math genius riddle

Please find the Vault code consisting of 5 different numbers … (1-9) …
1. The sum of the first digit and the sum of the third digit is 10 ..
2. The first digit is a square of the fifth digit
3. The fourth digit is equal to the second digit plus 1
4. The sum of the digits is 22

What is the Vault code?

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SherlockHolmes Expert Asked on 16th October 2017 in Adobe Interview Puzzles.
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  • 2 Answer(s)
    Best answer

    Answer– 94153

    Explanation-
    Let the number be VWXYZ

    Conditions:

    (1) V + X = 10
    (2) V = Z^2 => V = 4 / 9 and Z = 2 / 3  (V = 1 => Z = 1 which is NOT allowed.) 
    (3) Y = W + 1
    (4) V + W + X + Y + Z = 22

    Applying (1) and (3) in (4) => 10 + 2W + 1 + Z = 22

    => 2W + Z = 11   (5)

    Exploring possible values from (2):

    (a) If V = 4, Z = 2 then (5) =>  2W = 9 which is Impossible.
    (b) If V = 9, Z = 3 then X = 1, W = 4, Y = 5.

    Hence the code is 94153.

    Viji_Pinarayi Expert Answered on 17th October 2017.
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    Answer:94153
    We know that the answer will have the following pattern.
    x       y       10-x      y+1       sq.root(x)
    We know that x cannot be taken as 5 as 5^2=25>22.
    If we take x as 4^2=16,
    1st digit=16
    5th digit=4
    16+4=20
    only 2 is left and thus it is not possible.
    Only if  x is taken as 3 will we get a correct answer .

    ermordung Starter Answered on 31st October 2017.
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