If you're looking to do serious data mining and algorithm development, work with outstanding people, and solve incredibly difficult computation and machine learning problems - all while revolutionizing our $2.4 trillion health care industry by empowering consumers - this is the place for you.
Castlight Health is looking for an algorithm architect who can take the reins of some of our data mining efforts. An ideal candidate has a strong mathematics background, and has a penchant for applying novel algorithms to messy data, to find the valuable gems of knowledge hidden within. We would love to see a PhD in a relevant field, or several years of industry analytics work.
Let us know if this sounds like your kind of environment and you want to join our team.
In addition to a resume and a note about yourself, please send us a solution to one of the puzzles below. Please apply directly on our careers page at: www.castlighthealth.com/careers.
AN ENCHANTED HAT
At a particular school, an enchanted hat assigns each incoming student to one of four residential houses. School lore says that the hat sorts students into houses entirely on the basis of personality and moral character. But this year, a rumor is circulating that the hat actually assigns each student completely randomly.
The Headmaster hopes to disprove the rumor and reasons that if she can show the hat's assignments to be somewhat predictable, it cannot be assigning randomly. Before the students are sorted, she speaks with each student and privately writes down her prediction of which house that student will be assigned to.
What is the smallest number of students (m) that allows her to make one incorrect prediction yet still establish a high level of confidence (say, 99% certainty) that the hat is not completely random in its sorting?
If the headmaster's predictions are always wrong, would a sufficient number of wrong predictions (w) disprove the rumor with similarly high confidence?
ODD BAG OUT
You have 5 unmarked bags with 100 beads each. Bags #1-4 contain 4 red beads and 96 black beads; bag #5 contains 7 red beads and 93 black beads. You randomly select one of the five bags and remove three beads without looking inside the bag. One is red, and the other two are black. What is the probability that you drew the beads from bag #5?
Return the three beads to the bag and give it a good shake to mix things up. In the best-case scenario, what is the minimum number of beads you can withdraw, one at a time, to identify this bag as bag #5 with at least 50% certainty?