Average Salary Scramble

Nov 09, 2002

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?


TOM: Hmm.

RAY: And I think I may have hinted that the boss was a red herring, and he is. You don't have to know any of that stuff. I had to unclarify.

TOM: Unclarify, declarify.

RAY: And obfuscate. 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 is his salary and what part of that is the made up number. He then adds his salary to that 8500 and whispers it to the guy next to him.

TOM: Yeah.

RAY: Down the line. Finally the seventh guy has this huge number and he obviously adds his salary to it.

TOM: And he gives it back to guy number one.

RAY: He gives it back to guy number one. Guy number one subtracts the 8000 or whatever it is he added, divides by seven, and hence the average salary, and nobody knows nothing, and nobody gets hurt. And so we have a winner?

TOM: You bet we do. The winner is Allen Womack from Kushada, Louisiana.

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