9.3. The number 2019 is represented as the sum of different odd natural numbers. What is the maximum possible number of addends?
Answer: 43.

Solution. Evaluation. Let's calculate the sum of the 45 smallest odd natural numbers: 1 + 3 + ... + 87 + 89 = (1 + 89) / 2 * 45 = 2025 > 2019. Therefore, there are fewer than 45 addends, but the sum of 44 odd addends is an even number, so there are no more than 43 addends. Example. 2019 = 1 + 3 + ... + 81 + 83 + 255.

Evaluation Criteria.

“+” A complete and well-reasoned solution is provided

“土” A generally correct reasoning is provided, containing minor gaps or inaccuracies

“干” The correct answer and correct evaluation are provided, but the example is missing

“干” The correct answer and correct example are provided, but the evaluation is missing or incorrect

“-” Only the answer is provided

“-” The problem is not solved or is solved incorrectly