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   Who will be the lucky one?
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   Author  Topic: Who will be the lucky one?  (Read 660 times)
Altamira_64
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Who will be the lucky one?  
« on: May 9th, 2016, 7:30am »
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The sales manager in a big firm, after an exhausting but successful campaign, advises his staff of 20 employees that they can take the following day off to relax, but the leave day would be charged to only one of them, and he explained them to which of the employees he would charge the leave day.
Obviously all the employees were desperate for some rest, provided, however, that it would not be them to be charged with the day off, but the manager would want the contrary, i.e. to ensure that as many employees as possible will come to work!
Can you guess what was the manager's announcement as to which of the 20 employees would be charged with the day off?
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rmsgrey
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Re: Who will be the lucky one?  
« Reply #1 on: May 9th, 2016, 8:00am »
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on May 9th, 2016, 7:30am, Altamira_64 wrote:
The sales manager in a big firm, after an exhausting but successful campaign, advises his staff of 20 employees that they can take the following day off to relax, but the leave day would be charged to only one of them, and he explained them to which of the employees he would charge the leave day.
Obviously all the employees were desperate for some rest, provided, however, that it would not be them to be charged with the day off, but the manager would want the contrary, i.e. to ensure that as many employees as possible will come to work!
Can you guess what was the manager's announcement as to which of the 20 employees would be charged with the day off?

 
One possibility:
 
hidden:
Of those who take the leave day, the one who was hired most recently will be charged the day.

 
Analysis:
 
hidden:
Provided there is some public list, with the earliest person on the list who takes the day off getting charged the day, you can apply induction:
 
Assuming a given employee knows that no-one earlier on the list is going to take the day off (either because the employees have discussed the matter, or because they've analysed the situation and deduced the likely behaviour) they're faced with the choice of either getting charged the day, or coming in to work. Since they only want to take the day off if they're not getting charged it, that employee will come in.
 
Since the list is well-ordered, and no employee wants to be the first on the list to take the day off, no-one will take the day off.
 
Where things get interesting is when a little uncertainty creeps in - if each employee has a probability, p, of taking the day off anyway, and a threshold q, where once the probability of them being charged with the day off drops below q, they always take the day off, then only some of the employees will turn up, with the number depending on p and q.
« Last Edit: May 9th, 2016, 8:01am by rmsgrey » IP Logged
Altamira_64
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Re: Who will be the lucky one?  
« Reply #2 on: May 10th, 2016, 1:07am »
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Maybe something else that will also take into consideration the number of the employees (20)?
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