A number has three distinct digits. The sum of the digits equals the product of the digits. How many three-digit numbers satisfy this condition?
I think only one number can do: 123. 1+2+3=1*2*3=6
still no ideas of your own?
Try google when you have no clue:
http://math.stackexchange.com/questions/202679/sum-of-digits-and-product-of-digits-is-equal-3-digit-number
123 works 1+2+3=1*2*3=6 so that means 123,132,213,231,312,321 all also work.
To find the number of three-digit numbers that satisfy the condition, we need to determine the possible values for each digit.
Let's assume the three digits of the number are A, B, and C.
Given that the sum of the digits equals the product of the digits, we can set up the following equation:
A + B + C = A * B * C
Now, let's analyze the possible values for A, B, and C:
1. A cannot be 0 (since it's a three-digit number).
2. The maximum value for A, B, and C can be 9 (as there is no restriction mentioned).
We can now systematically evaluate the possible values for each digit and check if they satisfy the equation.
Starting with A = 1, we substitute it into the equation A + B + C = A * B * C:
1 + B + C = 1 * B * C
B + C = B * C
Since B and C must be distinct, B can be 2, 3, or 4. By substituting these values for B and C into the equation, we can check if they satisfy the equation.
By continuing this process for each possible value of A (up to A = 9) and checking the values of B and C that satisfy the equation, we can determine the total number of three-digit numbers that satisfy the condition.
Therefore, to find the answer, we need to solve the equation for every possible combination of A, B, and C and count the number of valid solutions.