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13 August 2008

Brain Teaser

One of the cool things about my job is that once in a while, my boss will throw some sort of ridiculous brain teaser my way, just to keep me sharp. I was digging through some old stuff because I recently switched offices (movin' on up...) and found this one, which I remembered thinking about for days before solving it drunk on over-sized mudslides at a Dallas BBQ. So I looked at it again, and for the life of me couldn't remember where to start for another day. This shit is hard.
Working alone, Holmes puts two coats of paint on a wall, one before lunch and one after lunch. One day, Holmes began at the usual time, and two hours before lunch he was joined by Watson, who paints at the rate of 600 square meters per day, and who left when they finished the first coat. Holmes promptly began the second coat, and then he broke for lunch at the usual time. One hour before his normal quitting time, Holmes had painted a second coat everywhere except where Watson had painted that morning. If each man works at a constant rate, what was the area of the wall, in square meters?
Have at it, if you dare.


  1. I am seriously going to solve this... so don't post a solution yet! I tried doing it last night a certain way which gave me 3 variables to solve for but I only had 2 equations so I spent all night trying to wrangle a third one out of it... but I'm pretty convinced now that you only gave me two relations there so I'm trying it a different way today. We'll see what happens I guess.

  2. Don't worry, I won't post the solution for a while, yet. But I assure you, there is one :)

  3. that was pretty straightforward. i was expecting something harder, but not quite this hard: all i'll say is that watson is a slacker compared to holmes, but 600 m^2 of painting in one day sure sounds like a lot of work.

  4. I think I got it... before, I was really getting hung up on how long Holmes's usual day is, but as long as 600 m^2 per day for Watson means that if he had Holmes's job he could only cover a 300 m^2 wall then I now see how that doesn't matter. ...I think.

    (In fact, I actually had the answer within a couple of hours of starting the problem, I was just a moron about units and didn't get to look at it again until today. Shows what good a solid background in physics *REALLY* does for your problem solving ability.)

  5. Yeah, one of the reasons this is so hard (there are a few, I think) is that it seems like you just don't have enough information. Anyway, I'm glad to hear you got it (if you want to be sure, you can email me for a poorly explained solution).

  6. please post the solution!