A basic but tricky number theory question

Math Junior
1

Problem:

Ahmed has small, medium, and large juice boxes containing:

  • Small box: 14 liters

  • Medium box: 21 liters

  • Large box: 35 liters

He wants to fill equal-sized crates with no leftover juice.

  1. Determine the possible number of boxes of each type that can be used to fill the crates.

  2. Find the largest crate size that ensures complete distribution.

  3. Identify which boxes must be in even quantity and which can be odd. Explain your reasoning.