Without taking the hint into account, there are two more numbers satifying condition 1:

1 : sum of digits is 1 and 1 * 1 = 1 81 : sum of digits is 9 and 9 * 9 = 81

Neigther of them satifies the second condition.

## mystery number

Without taking the hint into account, there are two more numbers satifying condition 1:

1 : sum of digits is 1 and 1 * 1 = 1

81 : sum of digits is 9 and 9 * 9 = 81

Neigther of them satifies the second condition.