A boy forget his pin code which was of 5 digits?

Answer 1

1st Digit: a= b*b

2nd Digit: b + c= 10

3rd Digit: d = b + 1

4th Digit: e + c = 14

Sum of all digits: a + b + c + d + e = 30

lets take 4th digit

e + c =14, so we can write it as

e + (10 -b) = 14

e - b = 4

e = 4 + b or e = b + 4

so here we go, sum of all digits

a + b + c + d + e = 30

b*b + 10 + b + 1 + b + 4 = 30

b*b + 2b + 15 = 30

b*b + 2b -15 = 0 (quadratic equations, 5 and -3 are the factors)

b*b + 5b - 3b - 15 = 0

b(b+5) -3(b + 5) = 0

b+5 = 0 or b - 3 = 0

b = -5 or b = 3 (avoid the -ve value)

so b = 3 and substitute in the original variables

1st Digit - a = b*b = 3*3 = 9

2nd Digit - b = 3

3rd Digit - b + c = 10, 3 + c = 10, c = 7

4th Digit - d = b + 1, d = 4

5th Digit - e + c = 14, e + 7 = 14, e = 7

so the 5 digit code is 93747