February 2016 Problem of the Month

Problem 1: One day two mathematicians, Issac and Sarah, meet in the street. "How are you? How are your sons?" asks Issac. "You have three sons as I remember, don' t you? I have forgotten their ages." "Yes, I do have three sons," replies Sarah. "The product of their ages is equal to 36." Looking around and then pointing to a nearby house, Sarah says, "The sums of their ages is equal to the number of windows in the building over there." Issac thinks for a minute and then responds, "Listen, Sarah, I cannot find the ages of your sons." "Oh, I am very sorry," says Sarah. "I forgot to tell you that my oldest son has red hair." Now Issac is able to find the ages of the brothers. Can you?

Correct solutions received from: Conan Zhao, Mauricio Bustamante, Andrew Mah, Phillip Harmon, Hannah Hall, Max Rezek, and Prof. Scott Hoover.

Problem 2: What is the value of:
\[\sqrt{2+ \sqrt{2+ \sqrt{2+ \sqrt{2+ \sqrt{2+ \dots}}}}}\]

Correct solutions received from: Conan Zhao, Mauricio Bustamante, Jamie White, Matt Kiser, Phillip Harmon, Hannah Hall, and Prof. Scott Hoover.

Problem 3: An apartment building has seven elevators, each stopping at no more than six floors. If it is possible to go from any one floor to any other floor without changing elevators, what is the maximum number of floors in the building?

Correct solution received from: Prof. Scott Hoover.

Submit solutions to Mitch Keller (Robinson 206) or Beedle Hinely (Robinson 113A) no later than noon on 29 February 2016. Good luck!