Question

Solve this puzzle
A man has forgotten his 4 digits ATM PIN.
Help him to recover
Some hints are as follows

1. First digit is half of third digit
2. The sum of second and third digit is 8
3. Fourth digit is the multiplication of first and second digit
4. Sum of all four digits is 12.​

Answer 1

Answer:

let ,

3rd digit is X

acq 2nd digit is 8-X

1st digit is X/2

4th digit is X/2 × 8-X=(8x-x²)/2

According to question X/2 +(8-X)+X+(8x-x²)/2=12

=>(x+16-2x+2x+8x-x²)/2=12

=>16+9x-x²= 24

=>x²-9x+8=0

=>x²-8x-x+8=0

(x-8)(x-1)=0

x is 8 or 1

The digit is 4080

We can't taken 1 as 3rd digit bcz 1st digit is half of 3rd so .

Answer 2

The pincode is 4080.

Given :

1. First digit is half of third digit

2. The sum of second and third digit is 8

3. Fourth digit is the multiplication of first and second digit

4. Sum of all four digits is 12.

To find :

4 digits ATM pin code of the man

Solution :

Let the third digit be x

Therefore, first digit = x/2

Second digit = 8 - x

Fourth digit = x/2 * (8-x)

= 4x - x^2 /2

According to the problem,

x + x/2 + ( 4x - x^2 /2 ) + (8-x) = 12

=> x + x/2 + 4x - x^2 /2 + 8-x= 12

=> 16 + 8x + x^2 =24

=>x^2 - 9x + 8 = 24

=>x^2 - 8x-x + 8 =24

=> (x-8)(x-1)=0

Therefore x is either 8 or 1

We cannot take the value as 1 as first digit is half of the third.

Third digit = 8

First digit = 8/2 = 4

Second digit = 8-8 = 0

Automatically fourth digit is also 0 as the sum of all digits is 12

Therefore the pincode is 4080.

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