Question

What is the sum of all the positive three-digit numbers whose digits are all odd?\?

Answer 1

The correct answer: Still an odd number.

Odd numbers added together are still odd numbers. It still works even if we add a million digit odd number and add it to 3. So, adding all 3-digit odd numbers together will still yield an odd number. Here is an example:

We will be adding 7 3-digit odd number samples from 100, 200, and 300. And then we will be adding the results just to see if it will become odd or even.

101 + 103 + 105 + 107 + 109 + 111 + 113 = 749 <--- Odd
201 + 203 + 205 + 207 + 209 + 211 + 213 = 1449 <--- Odd
301 + 303 + 305 + 307 + 309 + 311 + 313 = 2149 < --- Odd

Now, let us add the results.

749 + 1449 + 2149 = 4347 <--- Still odd

Based on our little experiment, the answer is still odd. In my opinion, for us to change the result of adding all 3-digit odd numbers to even, we must multiply the result to 2 or by adding the result by itself. Example A + A = 2A.