Find the sum of all 3-digit positive numbers N that satisfy the condition that the digit sum of N is 3 times the digit sum of N+3.
Details and assumptions
The digit sum of a number is the sum of all its digits. For example, 1123 has a digit sum of 1+1+2+3=7.
The number 12=012 is a 2-digit number, not a 3-digit number.
Which number line shows the correct way to find the sum p+q if p is positive and q is negative?
the answer is
your mom
To find the sum of all 3-digit positive numbers N that satisfy the given condition, we need to go through a step-by-step process:
1. Find the condition for the digit sum of N and N+3:
Let S(N) be the digit sum of N, so S(N+3) will be the digit sum of N+3. According to the given condition, we have: S(N) = 3 * S(N+3).
2. Understand the possible range of values for N:
Since we are looking for 3-digit positive numbers, N should be greater than or equal to 100 and less than or equal to 999.
3. Analyze the possible values for N:
To find the possible values for N, we can start by considering the smallest 3-digit number, which is 100. We can iterate through all the numbers from 100 to 999 and check if they satisfy the given condition. If they do, we can add them to a running sum.
4. Implement the algorithm:
Here's one possible algorithm in Python:
```
# Function to calculate the digit sum of a number
def digit_sum(n):
return sum(map(int, str(n)))
# Initialize the running sum
sum_of_numbers = 0
# Iterate through all 3-digit numbers
for N in range(100, 1000):
if digit_sum(N) == 3 * digit_sum(N+3):
sum_of_numbers += N
# Print the final sum
print(sum_of_numbers)
```
This code calculates the digit sum of each number N and checks if it satisfies the given condition. If it does, it adds N to the running sum. Finally, it prints the sum of all numbers that satisfy the condition.
Note: You can run this code in any Python environment to get the answer.