# Sakib Knows The Number!

Ragib: I got digits of a 2 digit number

Sakib: Is it an odd?

Ragib: Yes. Moreover, the sum of the digits of the number is a prime!

Sakib: The difference of the digits of the number is also a prime?

Ragib: Of course! Last of all, the multiply of the digits is equal to one of the digits!!

Sakib: Oh no! I know the number. It’s your roll number!

What is that number!

The digits may be 1,2,3,4,5,6,7,8,9,0.

Since two digit number, 0 can only be put in the second digit position.

But that will make the number even. So 0 is not any of the digits!!

1* any digit=1 or the digit

2*any digit(not 1) = not 2 or not the digit

3*any digit(not 1) = not 3 or not the digit

4*any digit(not 1) = not 4 or not the digit

5*any digit(not 1) = not 5 or not the digit

6*any digit(not 1) = not 6 or not the digit

7*any digit(not 1) = not 7 or not the digit

8*any digit(not 1) = not 8 or not the digit

9*any digit(not 1) = not 9 or not the digit

So its clear one digit is 1.

So the number may be 11,21,31,41,51,61,71,81,91.

But the sum of the 2 digit is also a prime!

So 31,51,71,81,91 will be ignored!

Now the answer may be 11,21,41,61

But the difference of the digit also is a prime!!

So 11,21 will be ignored!!!!

So the answer is 41/61…..

What a puzzle…!!!

numbers that follow odd and sum of digits is a prime are :11,21,23,25,29,41,43,49,61,65,67,83,85.

among these numbers follows “difference of digits also prime” are : 25,29,41,47,49,61,83,85.

last but not least , product of digits is same as one of it’s digits means one digit should be 1.

So Answer is 41 or 61.

### Your Answer

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