Magic V

Why I like this problem: This is another problem with a lot of variation, since the arms of the V can be extended to include more numbers, and the range of numbers can be changed. 

Observations from class: To make trial and error easier and more pleasant, I printed copies of the V and put them in dry erase pockets. While some students actually tried to find all of the possible solutions, a few remembered the Chipotle Combinations problem we did the week before and applied the strategies they developed in that problem to this one to figure out how many possibilities there were. I hadn't even thought of this link myself, so I was pleasantly surprised to see the transfer of strategies. 

Follow-up questions I asked: 

1. Can you figure out a pattern to make finding all the possibilities systematic?
2. How does the first number of the range affect the solutions? 
3. Does it matter if the range starts with an even or odd number?
4. How does changing the arm length affect the number of solutions you have?

Required skills / content: Adding numbers. 

Links: PDF 

Source: https://nrich.maths.org/