Positive Differences

This problem requires students to work systematically, and to construct convincing arguments as they consider which options are possible and which are impossible. 

Here are some questions for students to think about:

• What is the maximum difference you can make from two of the numbers $1, 2, 3, 4, 5, 6?$
• If $5$ was at the top, which numbers would have to be in the middle row?
• If $4$ was at the top, which numbers could we have in the middle row?  
• Can $4$ and $5$ both be in the middle row?
• Can $4, 5$ and $6$ all be on the bottom row?

This problem featured in the NRICH Secondary webinar in April 2022.