Crack The Code RIddle: What is the 5 Digit Pin Number.
Read the hints given in the riddle and guess the lady’s 5 digit pin number.
A house wife forgot her bank account PIN which is five digits’ number, but luckily she remembered some hints on how to recall this PIN.
Here are some of the clues
1) The 1st digit is a square of the 2nd
2) The sum of the 2nd and 3rd is 10
3) The 4th is equal to the 2nd plus 1
4) The 3rd and the 5th makes 14
5) The sum of all the digits is 30
What is the PIN?
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Let the 5 digits of the pin be a, b, c, d & e.
From the given statements we can write the following;
1) The 1st digit is a square of the 2nd
a = b^2
2) The sum of the 2nd and 3rd is 10
b + c = 10
3) The 4th is equal to the 2nd plus 1
d = b + 1
4) The 3rd and the 5th makes 14
c + e = 14
5) The sum of all the digits is 30
a + b + c + d + e = 30.
Let’s solve the first 4 equations to represent all letters in terms of b;
The 1) already is;
a = b^2. —- (6)
From 2) we can write;
c = 10 – b —- (7)
3) is already
d = b + 1 —- (8)
From 4) we can write;
e =14 – c —- (9)
From (7)
e = 14 – (10 – b) = 14 – 10 + b;
e = 4 + b —- (10)
Now substituting all the values in 5) we get;
a + b + c + d + e = 30.
b^2 + b + (10 – b) + (b + 1) + (4 + b) = 30
Solving this we get;
b^2 + 2b + 15 = 30
b^2 + 2b – 15 = 0
(b – 3)(b + 5) = 0
So b is either equal to 3 or -5;
Pin cannot be negative so;
b = 3
Now we can find all the other letters as;
a = b^2 = 3^2 = 9 9
a = 9
c = 10 – b = 10 – 3 = 7
c = 7
d = b + 1 = 1 3 + 1 = 4
d = 4
e = 4 + b = 4 + 3 = 7
e = 7
So the pin is 93747