The Coney Island Crab Cake Company

Jan 28, 2012

RAY: The seven employees of the Coney Island Crab Cake Company are sitting in the lunchroom having lunch, when they decide that they would like to know the average salary at the company.

Obviously, each person could write down his salary, they could add the salaries and divide by seven. But, they don't want to do that because nobody wants to divulge his salary.

As luck would have it, the boss enters the lunchroom. The employees ask if he can tell them the average salary. He says, "No, but I can tell you the highest salary and the lowest. And I can tell you that none of you earn the same amount. But I can't tell you what the average salary is-- you'll have to figure that out for yourselves. "

Here's my question. Is there a way for these seven people in the lunchroom to figure out what the average salary is, without divulging anyone's salary AND without discovering the highest and lowest salaries?

RAY: Here's how you do it. The first guy takes his salary and to it adds some number that he plucks out of the air. Let's say his salary is 500 bucks a week. He adds 8000 to it. He turns to the guy next to him and whispers, "8500," in his ear.
Now that guy doesn't know anything. He doesn't know what part of that number is the first guy's salary and what part of it is the made up number. He then adds his salary to that 8500 and whispers it to the next guy.
TOM: Yeah.
RAY: This goes down the line. Finally the seventh guy has this huge number and he adds his salary to it. And then he whispers the number back to the first guy. Guy number one then subtracts the 8000 that he had added, divides by seven (number of people in the room), and hence the average salary, and nobody knows nothing, and nobody gets hurt. And so we have a winner?
TOM: Very good! You bet we do have a winner. The winner is Allen Womack from Kushada, Louisiana. Congratulations Allen!

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