Ok, there’s 7 employees gathered together at a table and they want to figure out the average salary without anyone divulging their own salary.
Two questions to clarify the puzzler. I’m clueless on this one so far:
Does this mean no one can divulge their salary to any other person in the group, even if their salary cannot be linked to them personally?
The manager says he knows the highest and lowest salaries, but the puzzle seems to say the group must not discover these numbers. If so, is there a point that the manage knows these?
I’m assuming the employees can ask each other questions, but can the employees ask the manager questions?
What is the total payroll? How many employees?
As I read the puzzler, there are only 7 employees. If all 7 employees made the same salary, the average would be obvious to the employees. However, it was stated that the salaries are all different. Now if one knows the highest salary and the lowest salary, one would know the median salary. The puzzler, though, calls for one to know the average salary which I presume is the mean salary. This tells me that the median salary and the mean salary must be equal.
The employees then question each other by one asking the question “How many earn above a certain amount?” Each employee writes “Yes” or “No” on a piece of paper without divulging his name. The number of people above the amount is recorded. The question is then repeated with a higher amount. The amount is increased in equal intervals. This continues until there are three “Yes” votes and four “No” votes. The averaage salary is then the amount between the amount that generated four “Yes” votes and the amount that generated three “Yes” votes. One can continue selecting amounts between the one that elicited four “Yes” votes and three “Yes” votes to pin down the average value. In this way, nobody divulges his salary.
Now if one knows the highest salary and the lowest salary, one would know the median salary.
No you wouldn’t. That doesn’t make any sense. Suppose you had seven salaries that were:
1 - $25,000
2 - $30,000
3 - $50,000
4 - $55,000
5 - $80,000
6 - $90,000
7 - $100,000
The median salary there is $55,000. How do you get that from only the lowest (25,000) and highest (100,000) salaries?
Don’t worry about trying to answer that – the answer is you don’t get the median from only the highest and lowest values
…Each employee writes “Yes” or “No” on a piece of paper without divulging his name. The number of people above the amount is recorded. The question is then repeated with a higher amount…
Nah. I won’t explain how it’s solved, but the concept behind this puzzle is not an uncommon one. A little Google searching and you can find similar examples (and the solutions) on sites that offer mathematical puzzles.
You are right–I don’t know what I was thinking. One couldn’t get the median salary from knowing the lowest and the highest.
I’ll rethink the problem.
My quick-and-dirty solution (which will not win any prizes): everyone agrees that, tomorrow, he/she will bring 1/7 of his/her salary in Monopoly money, and deposit it into a box. Someone then counts the contents of the box, and that is the average salary. Granted, if one’s salary is not evenly divisible by 7, then the result will be off a little (unless they use play money coins to get to within the nearest cent). (I’m sure the unwritten rules of the puzzler require that they be able to calculate the average now, rather than tomorrow.)
The solution is the same as it was the other time(s) they used this one. “Pretty cute, huh?” (That phrase grates on me, please stop.)
Thanks for the comments. I thought about this week’s puzzler last night, and “eureka”, it can be solved exactly as stated on the Car Talk web site. The only hint I’ll give is that the sol’n is easier than last week’s puzzler.
Last week’s threw me for a loop. I thought and thought and finally found a pattern and then a sol’n which matched the sequence, but the sol’n I knew wasn’t the correct one, as the pattern was too complex. (My sol’n was 78; there’s a reason why 78 could be an answer; anybody else come up w/78?). Anyway, then when I heard the answer was 72, I was all-slapping-my-head-silly what a dummy I was for not thinking of it! Mental note: On these sequences, you can’t just look at the numbers themselves, you gotta look at their neighbors too.
This week’s puzzler is a good one. Think on it a while and you’ll likely get it – think what you need to know at the very minimum to find the average of a set of numbers – and I think you’ll figure it out.