I am about to join my Computer Science Master’s course in around 10 days. One of the introductory and how-to mails I received mentioned that hostel rooms are allotted by drawing lots. One of the hostels is a newly constructed block, which has slightly better rooms than the others. This situation posed an interesting problem to me: how to maximize my chances of ending up in the new hostel?
Or, phrasing in a more general way:
There are p lots, out of which q are winning lots (0 < q ≤ p). Contestants draw their lots one after the other. After drawing his lot, the contestant publicizes the lot that he has got, i.e. whether it is a winning lot or not. A lot once drawn is not returned to the box. What is the ideal time to draw your lot, so as to maximize the winning probability?
Continue reading The Hostel Lot Problem
For a while now, I’ve been contemplating about buying myself a whiteboard. While I was not under the illusion that a whiteboard in my room was somehow going to magically boost my creativity and productive thought; I was pretty curious, given the visual thinker that I am, what a large, solid drawing surface could do to help map my thoughts out. Thus, given that entry-level whiteboards where not prohibitively costly anyway, I decided to take a plunge and brought myself a 2’ x 3’ whiteboard and a couple or markers to test my hypotheses out.
Within three days of having the board on my wall, I find myself reeling for it quite more often than I had anticipated. First of all, the novelty of a whiteboard (I quite love the feel of the bullet-tip felt pen in the slippery surface) prompts me to write things a lot more often than I otherwise would. While watching a video-lecture, for instance, when I encounter a formula that I have a doubt about, I could pause the video and try deriving the formula myself until I’m convinced. Also given the pathetically absent-minded bloke that I am (worse, I typically go over a sum over and over wondering what’s wrong; without realizing that I’ve written 2 x 4 = 6 somewhere along the way), a whiteboard makes it easier to spot mistakes — I could just take a step back and look at the derivation, and in the second or third try, the error usually pops up to me.
Better still, I’ve started working away at problems (mostly insignificant fancies) that pop up in my mind randomly, problems which I would otherwise have put off indefinitely. With the whiteboard, I can now grab my marker when my mind starts to wonder, ‘why doesn’t anybody talk about an edge-list representation of graphs yet, where you simply store the list of edges’ ; I can instantly grab my pen and start working out the data structure and trying to build BFS and DFS algorithms on it until I’m finally convinced why it is a bad idea (there is little gain in the edge-list representation, most of the things the edge-list is good at, the adjacency list performs equally better; while the algorithms are slightly less efficient on edge-lists).
To sum things up, even though the whiteboard did not ‘magically’ boost my creativity, it did so to a non-trivial extend — mainly, it turned my otherwise lazy thought-process pro-active. I consider the whiteboard expense money well spent.