This activity is an introduction to permutations, combinations and discreet mathematics.

Part 1: https://teacher.desmos.com/activitybuilder/custom/61cd0d782f7ddbd7a8698c08

Part 2: https://teacher.desmos.com/activitybuilder/custom/61cde7805c82cb0a114e355b

Part 3: https://teacher.desmos.com/activitybuilder/custom/61d10450c4f5850a3d8056c1

Questions

1. You've been given enough materials to pave 52 miles of trails between the seven towns of Mathlantis. Will you have enough materials to connect each town?
2. Determine all the possible routes between each of the 7 towns. How many are there?
3. Where will your shortest-route path end and begin?
4. Will a continuous or non-continuous road be shorter?
5. What is the shortest loop-route that connects all 7 towns?

Original graph: https://www.desmos.com/calculator/lvnokthxjd