Find a three-digit number that satisfy following question.

Question

Find a three-digit number that satisfy the following condition:
The first digit and last digit differ by two.
The sum of first two digits is more than eight.
The difference of the last two digits is more than zero.
The product (multiplication) of fist digit and last digit is twenty one.
The product (multiplication) of first digit and second digit is more than ten.
The sum of last two digits is less than nine.
The sum of first two digits is less than ten.

Answer 1

 

The product of the first and last digit is 21.

So one of them MUST be 7 and the other 3.

 

 This contradicts the first criteria that

the first and last digit must differ by 2.