Puzzle of the Week #4

by Nolan Musslewhite '20

Solvers of last week’s puzzle (in order):    
    1. David Hla
    2. Liam Chalk
    3. Matthew Chalk
    4. Luke Dougherty
    5. Maggie Wang
    6. Jonathan Merril
    7. Mr. Rick DuPuy
    8. Robert Shekoyan

Answer to and commentary on Puzzle #3:

    Classification: Medium / Hard. Though the problem could be solved deductively by limit approximation, the best way to solve it was algebraically. First, we must solve for the nested fraction. The form 18/(7 + 18/(7 +18/(7 +18(/... can be evaluated with the equation y = 18/(7 + y). Solving quadratically gives the possible solutions 2 and -9, of which 2 is the only nontrivial solution (we are assuming the solution is real). Now, to solve for the nested radical:

we must solve for x = √(2 + x). Solving quadratically gives the possible solutions 2 and -1, of which 2 is the only possible solution, assuming a real number value for x.

Puzzle #4
Nolan Musslewhite (nmusslewhite@stalbansschool.org)

This week’s puzzle: Analytics / Logic. Aer O’Plane is a mischievous air traffic controller in Dublin, Ireland. He wants to prevent his old friend, Aer O’Port, from successfully completing a ‘round Ireland journey from Dublin to Cork, Shannon, Kerry, and Knock (in no particular order, save that the journey must start and end in Dublin) by canceling exactly one of O'Port's flights. That is, O’Port is trying to visit each of the aforementioned towns at least once in a single day (starting and ending in Dublin) by flying between them, and O’Plane is trying to make this impossible by canceling one of O’Port’s flights. Your task: find the exactly one flight that O’Plane must cancel to make it impossible for O’Port to visit all of the five airports in a day, using the following flight timetable (assume all flights last 1 hour and that at least 10 minutes are required for each of O’Port’s connections). 
Hint: Be organized!