Let S(N) denote the digit sum of the integer N. As N ranges over all 3-digit positive numbers, what value of N would give the minimum of M=N/S(N)?
This seems to be a programming challenge.
While this can probably be worked out in mathematical terms, it is easily shown by exhaustive search that the 3-digit number is 199, where the minimum quotient is
199/19
=10.47 approximately.
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To find the value of N that gives the minimum of M=N/S(N) as N ranges over all 3-digit positive numbers, we need to calculate the digit sum for each number and divide it by the number itself.
Here's how you can approach this problem:
1. Start by considering the first 3-digit positive number, which is 100.
2. Calculate the digit sum of 100 by adding its digits: 1 + 0 + 0 = 1.
3. Divide 100 by its digit sum: M = 100/1 = 100.
4. Keep track of the minimum M value found so far, which is initially 100.
5. Iterate through all the remaining 3-digit positive numbers (101 to 999).
6. For each number, calculate its digit sum.
7. Divide the number by its digit sum to get M.
8. If the calculated M is less than the minimum M value found so far, update the minimum M value and remember the corresponding number.
9. Repeat steps 5 to 8 for all 3-digit positive numbers.
10. After iterating through all the numbers, the final minimum M value will be the desired result.
Let's consider an example to make it clearer.
Starting with 100:
M = 100/1 = 100
Minimum M value so far: 100
Iterating through the remaining numbers:
For 101:
Digit sum = 1 + 0 + 1 = 2
M = 101/2 = 50.5
Minimum M value so far: 50.5
Continue this process until you've checked all 3-digit numbers.
After evaluating all the possible values for M, the number that corresponds to the minimum M value will be the answer to the question.