The Mean CEO

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Here is another puzzle from the mag that I get every 2 months – again, I don’t have the solution but will do some time down the track.

“In the beginning of the second half of the 21st century, the Society of Actuaries decided to change its education system once again. This time it offered an unlimited number of courses. If a candidate expressed a desire to learn any actuarial topic, he could do so. There were an unlimited number of topics because students were not restricted to a specified number of pages read in actuarial books or articles read on actuarial websites. Each topic was validated by an exam. In such a world, there are no ASA or FSA designations; instead, the number of exams passed determines the level of an actuary.

It is 2075, and this system has been a success

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Ok, so 21 views but no posts – hmmm – as I said I don’t have the answer to this puzzle but I do have some promising lines of enquiry.

Here are some possible solutions and / or comments …

1) Mr Purple randomly picks a number between 1 and 5555 and offers the job to that candidate – chance of being fired = 5554/5555
2) Given that each candidate has a different score, Mr Purple can eliminate any candidate that scores less than 5555
3) Mr Purple flips through the first 80 candidates, keeping track of the highest score. He keeps flipping through the candidates, updating the highest score and decides to offer the job to the 3rd candidate (after the first 80) who beats the current highest score – change of being fired is about 79%

Does anyone else have a possible solution and / or any comments?

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Ok may have got the wrong end of the stick here but here goes

1) Mr Purple can open file 1, open file 2. If file 2 is lower than close (delete), keep file 1 open and compare with file 3. If file 1 is lower than close/delete keep file 3 open. As long a Mr Purple has two files open to compare he will eventually by a process of elimination find the person with the highest score.

2) 0- as he will definitely get the highest score

3) No with this method

I may have overly simplified this though

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Jezza – my reading of …

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He opens a file, reads the number of exams passed, and closes it if he chooses not to hire the first candidate. Mr. Purple then opens the second file, reads it, and, again, closes it if he does not want to hire the second candidate.

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… doesn’t allow for your ‘have two files open at once’ method. I take the above to be that he needs to decide to hire / not hire each candidate without looking at future resumes.

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I thought you would say that … back soon

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Has anyone seen sdckapr, I thought that this puzzle would be right up his alley!

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I have been on vacation and am just now trying to catch up on my browsing activities from the past week before I go away for a few days next week for my daughter’s college orientation.

The puzzle has been an activity I have not been able to make time to think about…

Steve

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Here is the solution as published by the magazine (and I must say, although I have no proof, that this is the mathematical method that I was thinking about) …

1) Skip 2,043 candidates and remember the one with the highest number of exams passed (X). Then hire the next one with the number of exams passed greater than X. Surely, if there is no such person, Mr. Purple will get fired.
2) 63.21 percent, very close (but not exactly equal) to 1 – 1/e.
3) The probability of getting fired will start at 50 percent for three candidates, then goes down to 45.83 percent for four candidates, then keep going down and approaches 1 – 1/e. Since we talk discrete mathematics here, there is no 1 – 1/e limit per se.

This puzzle is an analog to a better-known Sultan Dowry puzzle. (In the Sultan puzzle there are 100 daughters with different dowries. Each daughter is shown to a commoner who can only marry the daughter with the highest dowry.)

Since no actual figures are given in the puzzle, the only useful information Mr. Purple has is the number of actuaries he has interviewed, the number of candidates to be interviewed, and the highest number of exams passed among those whom he has interviewed. It is evident that Mr. Purple will hire an actuary with a better exam

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Ahhh, I thought as much. I have similar calculations on my scratch pad now, yes, yes, I see, hmmm, clever use of 1 – 1/e very discrete indeed.

Yes, when I first saw this puzzle I immediately thought of the Sultan puzzle and his 100 daughters with different dowries

Seriously Tim, thanks for getting the answer and sharing, I am at a complete loss for words for once as I don’t understand a single word of the explanation

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yeah – it is a bit ‘light on’ regarding the workings of the solution. Its almost if as they said “ANSWER: obvously it is 2043” and left it at that. I’ll add more my thinking re mathematical solution and a more ‘political’ solution later tonight (after I bath the dogs – or is that too much info?).

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No, no, never too much information… what method of dog washing are you going to use; bath, shower or a good old fashioned hosepipe? What flavour shampoo are you going to use? Are you going to use conditioner? and if so will it be medicated?

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When I first reviewed this puzzle, I didn’t know where to start to answer it. The main sticking point was that I couldn’t get a handle on how Mr Purple can work out the top score.

I settled on letting Mr Purple sample the 5555 candidates to get a high score and then taking the next candidate that exceeds that high score. The question was, how do I turn this approach into an answer.

I used an excel simulation approach that randomly sorts the 5555 candidate scores and then record the probability of getting the top score if you same from the first ‘n’ candidates. I then had enough information to plot the initial sample size against the probability.

This gave me the following chart (30,000 simulations) – see below. As you can see, the highest probability is about 37% when the sampling size is about 1900.

Well, so much for a mathematically solution. My other thoughts were that the Mean CEO deliberately set Mr Purple up to fail and so he should turn the tables on the mean CEO. There are a number of ways of doing this – here are two.

1. Open the first resume and then go on a (sudden) vacation. When Mr Purple gets back (he makes sure it is after the mean CEO is back), he drops in on the mean CEO to refresh his memory on the top score and then returns to his desk and hires the person with that score.
2. Delegate the responsibility of hiring the ‘right’ person to the main person who reports to Mr Purple (and set out the same situation faced by Mr Purple – vis a via firing etc). Also suggest to this person that they might want to delegate this task to their subordinate (as well as suggesting the delegation). Finally, when this task has been delegated to the weekend after hours gardener (after being delegated to everyone else in between), the gardener makes a hiring decision and it proceeds back up the chain. When the CEO returns, he is presented with the situation (ie everyone’s job rides on hiring the person with the highest score) and that they have hired Person X with a Score S. Mean CEO can then either say ‘wrong’, fire everyone and ruin the business or say ‘correct’ – well done.

Re bath the dog (I just know that this will come back to me sometime later, a la pepsi shelf) – indoor bath room, one application of white lighting shampoo, no conditioner (unless going to dog show), towelled dry and then application of hair dryers (dixon – juk, dapple – no problem, she is deaf!). Dixon doesn’t like baths (will hide in the corner) but accepts them when I hold his collar – even steps into the bath with the look “ok, get it over with” – really, it is all a big show from him.

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Thanks Tim

Beginning to understand the concept when I read it through again last night, never been really good with the maths around these puzzles, I prefer my triangles, curves and spirals. Good work on your part anyway.

> I just know that this will come back to me sometime later, a la pepsi shelf

I was just concerned that you were going to tell me you bathed it in pepsi

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