My digits are the same. Their sum is 3 less than their products. Who am I?

33.

Same digits.
Sum: 3+3=6.
Products:3*3=9.
6=9-3. {Sum(6) is 3 less than products (9)}.

2x = x^2 - 3

x^2 - 2x - 3 = 0
(x-3)(x+2) = 0
x = 3 or -2, let's reject the negative answer

you are 33

To solve this problem, let's break it down step-by-step:

Step 1: Let's assume that the two digits are x and x (since they are the same).

Step 2: According to the given information, the sum of the digits is 3 less than their product. This can be represented as: x + x = (x * x) - 3.

Step 3: Simplify the equation: 2x = x^2 - 3.

Step 4: Rearrange the equation to set it equal to zero: x^2 - 2x - 3 = 0.

Step 5: Factor the quadratic equation: (x - 3)(x + 1) = 0.

Step 6: Set each factor equal to zero:

- x - 3 = 0 --> x = 3
- x + 1 = 0 --> x = -1

Step 7: Since the problem states that the digits are the same, the solution must be a positive number. Therefore, x = 3.

Step 8: Therefore, the two digits are 3 and 3.

So, you are the number 33.

To solve this puzzle, let's assign variables to each digit. Let's say the digits are a and b.

According to the given information, the digits are the same, so a = b.

The sum of the digits is 3 less than their product, which can be written as:
a + b = ab - 3

Since a = b, we can substitute a for b in the equation:
a + a = a * a - 3
2a = a² - 3

Now we can rearrange the equation to a quadratic form:
a² - 2a - 3 = 0

To solve this equation, we can factor it or use the quadratic formula. Factoring it, we get:
(a - 3)(a + 1) = 0

So, a = 3 or a = -1.

Since the digits cannot be negative, we conclude that a = 3.

Therefore, the mystery number is 33.