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## Deantini’s Brain-Buster

During the tree-lighting ceremony last Thursday on College Walk, our darn-diddley Dean added to the College’s finals-burden by announcing a little extra-curricular pop quiz. Though the quiz is merely a pesky distraction for our more SEAS-minded peers, Bwog is skittish (and uncomfortably reminded of consulting interviews). The Dean, however, says it’s something technical yet accessible.

The Dean’s Office wants submissions by December 14th, which you can leave in the comments of this post. The winner, or winners, get a free lunch with the dean.

**The quiz:**

How would you count the number of lights on the trees lining College Walk? Suggest a method for estimating them (not an estimate) that does NOT involve actually counting the lights.

*imposter Dean via screencrave*

## 42 Comments

@Here for a free lunch Estimate the number of lights in a strand, say about 100, because that’s usually what the box says. Then estimate the number of strands on one of the trees. Then multiply: 100 (number of lights/strand) * number of strands per tree * number of trees on college walk = number of lights on college walk!

Standard FroSci stuff right there.

@consulting answer? not terrible, but you need estimates for your estimates. Who’s to say your estimates for the estimates are good?

@Anonymous A back-of-the-envelope calculation

@Anonymous Base assumptions: -Lights are all on one string and are uniformly distributed, only going across each section of the tree once.

-The string is 0.1 meter thick, with lights are distanced 0.25 m away from each other on the string.

-Trees are perfect cylinders with eight branches sticking out that are also perfect cylinders.

-Tree trunks are 2 meters high and 0.25 meters thick. Branches are 1 meter long and 0.1 meters thick.

Calculations:

(Lateral) Area of Trunk = 2pi*radius*height = pi meters^2.

Length of string occupying that space = area/width = pi/0.1 = 10pi meters. 31.4 meters, with lights 0.25 m away from each other, equals about 125 lights on a trunk. Area of one branch = 2pi*0.1=0.2pi m^2. String length = 0.2pi/0.1 = 2pi = 6.24m, so about 25 lights on one branch * 8 branches = 200 lights. So that’s 325 lights on one tree times the number of trees.

@consulting answer? Sense checking. Do you seriously think there are only 325 lights on one tree?

@Anonymous Are the lights minis, 5mm LEDs, C7s, C9s or another variety? (“An African or European swallow?”)

@Anonymous Measure the lux (http://en.wikipedia.org/wiki/Lux, luminous emittance) of one lit tree at night. Look at manufacturing information for a single light, or measure the lux of one lit light. Assuming all trees have the same number of lights, LuxTree/LuxLight * Number of trees. If trees have different numbers of lights, measure the lux of each tree individually.

Alternatively, measure the lux at a point closest to equidistant from all the trees, then taking into account the individual distances from each tree, find the average lux from each tree. Again, LuxTree/LuxLight * Number of trees.

@yea but your method doesn’t take into account the lights that are already out, and the dean did NOT say “count the number of working lights”.

@Anonymous Count the number of boxes of lights purchased for purposes of lining the trees on College Walk (should be documented on an official receipt). Multiply by the amount of lights per box.

@consulting answer? What if you had to purchase all the lights for the job yet to be done? Say you were the contractor and had to purchase, with no returns because you have a tight deadline? Bad answer.

@Hmm... 1) Crowd-source back-of-the-envelope calculation that would be child’s play if you’d actually showed up to Fro-Sci

2) stroke SEAS students’ egos by suggesting that they’re better equipped to handle such a problem, in hopes that they’ll be more inclined to show off their knowledge

3) Abuse your newsblog’s moderation system to intercept promising answers

4) Use your newly gained advantage over the rest of the student body to keep that delicious dean cocktail all for yourself

I’m onto you, Bwog.

@consulting answer? Conniving and secrecy is definitely a tactic used in industry. However, the suggestion that 3) is legitimate amounts to cheating, not to mention disruption of trust in free speech. Won’t moralize though. We know what happens to insider traders

@Anonymous 1. record the amperes of light given off by all lights

2. record the amperes of light given off by one light

3. divide!

@Anonymous @Anonymous: Amperes (electric current) is consumed, lumens (luminous flux, i.e. light) is emitted.

@Anonymous ooops. revised standard edition:

1. record the total number of lumens

2. record the number of lumens given off by one lightbulb

3. divide!

@Anonymous @Anonymous: already been done. look at the above comments.

@consulting answer? Measurement of lumens is only truly accurate in dark space and without obstruction (i.e. tree leaves and the wire itself). This is a terrible idea out in the city of light pollution. Also, how would you deal with variation in lumens in the test light?

@CC '14er just look at how many are on ONE box then multiply that by the number of boxes they used :D

@wow everyone here’s a noob… has no one had consulting interviews?

@Anonymous Attach electrodes to that 1020 guy’s head and tell him that inside one of the lights is a tiny object that will unquestionably reveal the location of a date with Kristine that you have set up for him. Count the number of hopeful spikes in brain activity instead of counting lights.

@Anonymous Call up the maintenance guys and ask them.

@GS'14 Create a helical model for the amount of lights as a function of the length of the wire. Then, I would bend the rules:

1. Measure the length of the wire used because that’s not off-limits and plug that into the function.

2. Ask the dean (or anyone else who’d know) how much money was spent on the white Christmas lights because that’s not off limits. Use that to estimate the length of the wire and plug that into the function.

Otherwise, I would add a diameter variable to my model and take some measurements of one tree, counting branches and measuring their and the trunk’s diameters, then count the number of trees.

@wtf is wrong with you?

@GS/JTS'15 Count the number of plugs on a tree to determine the given number of light strands. Each strand has 100 lights. Multiply the number of strands by 100 to get the number of lights on a tree. Multiply that number by how many trees are lit on college walk. This strategy would work best during the day because it’s harder to see the plugs at night.

@Anonymous I’d find another school with a spotlight on awkwardness that was exactly ONE lumen less than the responses to this post and then…oh fuck it, I’m graduating in May. Have fun, suckas.

@Anonymous Ask the administration for the cost of the tree lights. Divide that cost by the average price of a box of 100 white lights. Multiply by 100.

@consulting answer? The administration is not likely to give you cost of lights only. They contract out work to a 3rd party, and they will likely invoice you an amount that includes taxes, net sales. Look at wholesale prices for the lights for costs of goods sold.

The better question would be to estimate the profit the 3rd party contractor made in stringing up all the lights. This is probably better from a contract management perspective to improve the university’s operational effectiveness. You could make assumptions for the activity-based operating expenses (i.e. overhead, allocated corporate charges), estimate # strings of lights on college walk * wholesale pricing per string, other direct inputs (i.e. labor costs), taxes. Then take the net out of total revenue on the contract.

@Bliss So here’s how I’d do it:

Stand around college walk for about an hour or two. When a person passes you by, kindly ask them how many lights they think are on the trees in total. Tell them they can estimate it however they’d like. Do this for as many people as you can within that set period of time. After the time elapses average all of the estimations people have given to you, and you’d probably get a pretty good answer.

@consulting answer? Surveys are widely used in consulting but never to replace a quantitative measure as easily calculable as estimating number of lights on college walk. You could introduce biases into your survey from dumb people who have no interest in completing an accurate exercise. Even if you incentivized your survey-takers, you would get an answer that is no smarter than a guess.

@Karim So just ask the people holding Calc books.

@alternate method Find watt rating of standard Xmas light bulb. Measure how many kWh were used over a period of time (let’s say an hour) from the plugs on college walk.

@consulting answer? Data based estimates are pretty good, in theory. How would you separate the KwH usage from the University’s total electricity bill?

The consultant would measure before and after energy usage before lights are put on. Then, this would help inform your total electricity usage. But, could you get more accurate than this?

Also, Deantini I suppose will be expecting this answer–no copying!

@Anonymous burn the tree down, then the number of lights would be zero.

@Anonymous Just Rainman that

@Anonymous Are you allowed to count the pixels?

@Anonymous this is IRL

@Anonymous Ask Siri

@consulting answer? But the student’s delight and not to mention the environmental, city/goverment, historical societies would be dissatisfied! I’m sure those trees are insured, are they not?

@why not? The question asks us how we would count the number of lights on the trees lining College Walk. Meaning that we are intended to figure out the present number of lights. How better to understand the present than to look at the past? To find the answer, one should gage the number of lights used in past years.

This could be done a myriad of ways, for instance with the use records of increased wattage on College Walk once the lights were turned on, or even a rough estimation from those who supplied and/or attached the lights to the trees. The University has most likely used the same lighting arrangement for most all of the 15 times this ceremony has been held and a simple calculation could find you the answer:

(lights used for year1 (1998) +…+ lights used for year14 (2011))/14

*I say 14, rather than 15, because this method looks back upon past years and not the current lighting arrangement. If the figures used for this equation included counting the lights, since this year’s number of lights is not included, it would still uphold the rule of not counting the lights on the present arrangement.

@anon (1) Pick a simple random sample of n trees. Enumerate the stands within each sampled tree, select a simple random sample of strands within trees. Count the lights on each of these strand. Use the formula for the mean and variance based on two-stage cluster sampling: http://webpages.uidaho.edu/~chrisw/stat422/TwoStageCluster1.pdf

(2) Pay a meth addict to count all of them. Twice.

@Karim Check the invoice.

@anon count the number of extension plugs on each tree (the ones used for stringing the lights together)

multiply by number of lights/string