- Near the bottom.
- Depends on the random variable's chance of telling the monkey to move up or down.
Does the monkey also throw a dart at the stock listing pages of the newspaper every day? 
I was thinking about the fact that the job market right now seems to be both a sellers market and a buyers market (using real estate terms here). Both, lots of jobs to choose from and lots of candidates for companies to choose from.
Despite a very low unemployment rate, companies are getting tons of applicants for their jobs. This is because the people applying are employed. The current work climate is such that there is no company or employee loyalty. So people change jobs more frequently and so there is more turnover. This also leads to companies wanting to find the perfect person (purple squirrel), who will stay for a while. People who maybe at another time wouldnât be thinking or making a job switch instead are applying to jobs that seem to be better (grass is greener and without companies providing pensions - not a lot of cost incentives to stay someplace a long time).
So overall, again using real estate terms, there are more transactions, as there is more job hiring in general, despite high employment levels. I look at LinkedIn profiles and will see somebody with 10 years of work experience and they have worked for 5 different companies in 5 different cities. and I donât think this is unusual.
The lengthy time it takes to go through the hiring process, as well as employers looking less favorably at currently unemployed people, also creates incentive to look for a new job while still employed â i.e. more incentive against loyalty.
- Correct.
- What if it is 50% up, 50% down?
- Near the bottom.
- 900 * 0.99^182 (except in a leap year, assuming first day is odd).
- Median is 1000 * 0.99^182.5, (in a non-leap year, assuming an infinitely tall pole), while the mean is (slightly) higher.
I think it would be better to ask this question as âstarting todayâŠâ and see if the candidates have the presence of mind to remember that 2020 is a leap year.
Question two trips up most people. The correct answer is ânear where it startedâ. So for the people who got it wrong, I ask them to accept that ânear where it startedâ is right, and figure out why it is right.
Presumably, your reasoning is that if the monkey is at height h, the expected change dh = 0 (1/2 * h /10 + 1/2 * (-h /10) ). So the expected sum of 365-366 days of dh = 0, giving an expected end height = starting height.
However, since the pole is of finite 2000 feet height, a monkey at h > 1818 feet who moves up will climb past the top of the pole, fall to the ground, and have h = 0 thereafter. This will bias the expected end height toward the bottom.
Even if the monkey is smarter and merely stops at the top instead of climbing past and falling, the expected dh is now < 0, which will bias the expected end height to be below the starting height.
Youâre hired @ucbalumnus.
How about the one on one lunch interview with a CEO. Urban legend or not. Not 100 percent sure.
CEO suggests to all interviewees to try the famous non controversial vegetable soup. If you say no. It said something about trying new things or not. Of course unless there is a food issue or allergy.
If you said yes. Which we would assume everyone would based on the circumstances.
They then asked if they would like salt or pepper when the soup arrived. Say yes. Interview over in terms of moving forward. They had a real issue of making choices prior investigation. Ie. Trying it first before following your habits.
@hebegebe , what kind of answers at what frequencies do you get from these questions?
But @hebegebe you are stating that the mean height of the monkey is near where it started (and as @ucbalumnus stated you also need an infinitely tall pole). You donât expect the monkey to be at the mean (ie âaverageâ) height, you expect the monkey to be at the median (ie âmost likelyâ) height.
For example after two days, the monkey is at 810 ft with 25% probability, 990 ft with 50% probability and 1210 ft with 25% probability. The mean is certainly 1000 ft but you expect the monkey to be at the median height of 990 ft. Extend that for another 363 days and the median is close to answer 1 (the bottom).
So you need to ask the question differently if you want the answer to be the mean height.
@ucbalumnus and @Twoin18 ,
The real value of the second question is the âwhyâ discussion that occurs after they provide the answer. The lack of an infinitely tall pole, the the difference between expected value and likely value, the distribution of possible outcomes, and the applicantsâs appreciation of how problem 1 and problem 2 are different tells me a lot about a personâs practical math skills. I am not bothered by someone not understanding the mean value formula right away, as long as a useful discussion follows.
Relating this back to the topic at hand, I believe puzzles, and for that matter interviews should start out easy and have increasing depth to them. I start out every interview stating I am going to keep asking harder questions on each topic until they are unable to answer, and then move onto another topic.
And yes âexpectedâ height has a formal mathematical meaning of mean. But you should expect to find the monkey near the bottom since 50% of the time it will be below the median, even if the âexpectedâ average height is 1000ft.
You completely understand it, @Twoin18 . Most candidates are stuck to the point that they canât tell that questions 1 and 2 are different in any way. I would be thrilled if they provided the answer you did, as you go well beyond the understanding of expected value to the more nuanced understanding of likely distribution.
@hebegebe Ha, I still remember being turned down for a job with a company that was responsible for electricity distribution because they worried I would be too interested in solving their problems of active demand/supply balancing (which admittedly were deeply fascinating, not least to the âsmartest guys in the roomâ at Enron who later managed to exploit the shortcomings of such a system) rather than managing the people who actually worked there.
There is a HUGE difference though in being asked a puzzle question orally in a situation such as an interview which comes with inherent stress and being asked the question in writing with the time to read it multiple times and contemplate the answer for awhile. 
I finally had a chance to read through the thread. My D is experiencing the same interview homework and ghosting on an exhaustive job search. She is applying in her creative industry and there are a lot of job openings but all require prior experience and very few jobs are for entry level.
Most of the jobs require a review of a 45 page script and a full synopsis and analysis turned in. Then another online or video test. Then an actual phone interview with a human!! Then ghosting for weeks. Finally, a frantic email requesting a face to face interview âtomorrowâ. Then ghosting. I think the final ghosting for weeks is because they are trying to hire their first choice and keep her stringing along.
She makes it to the final list but keeps losing out. She is getting so discouraged after all the work she puts into it. I feel sorry for her.
Reading about these laborious steps that @kiddie and @coralbrook 's daughters are having to go through with job applications, Iâm guessing these are larger companies? I could be wrong but maybe if the young women apply to smaller companies they wonât have to jump through so many hoops for those.
The ghosting is downright rude. It has always happened sometimes - even decades ago - but I think that practice is more prevalent now. Itâs very short sighted and unprofessional. When you think how much many companies spend on advertising and trying to protect their image, why not send a simple follow up? Iâd never run a company that way.
Actually it has been all sized companies. From startups with only a few hundred employees to larger companies (nationally known) with thousands of employees worldwide. @coralbrook nailed it, so frustrating to be asked to expend so much time and energy and then be treated so rudely. For my daughter, it means work on top of her already demanding job where she often puts in 12 hours days. Maybe both our girls will get a new job for Christmas this year!