Chapter 6.1, Problem 37MS

Here we celebrate the power of algebra as a powerful way of finding unknown quantities by naming them, of expressing infinitely many relationships and connections clearly and succinetly, and of uncovering pattern and structure.

Pigeon count. Mary runs every morning. She follows an Euler circuit through the park near her house. Along the first edge she sees one pigeon, along the second edge she sees three, along the third edge she sees five, and so on. If there arc ten edges total in Mary’s run, how many pigeons does she see? Find an expression that gives the total number of pigeons she would see if there were n edges in her run.