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# What is the average pay

## Question

You and two of your friends would like to know the average of all of your salaries.  You are each self-conscious about the amount of money you make and will not tell one another your salaries.  What can you do to figure out the average salary?

## 3 answers to this question

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Spoiler

You arrange with a friend to tell you the sum of three numbers, one each of which will be told him by the group. No mention is made to the friend of the meaning of the numbers. You each then tell the friend your salary, and you divide the sum the friend tells you by 3. You thus determine the average without telling one another your salaries.

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Without an outside person

Get some containers you can't see through with a slot. Sort of like a mini ballot box.  Mark one for each number place (ones, tens, hundreds, etc). Use something cheap like paper clips and place them in the containers according to your salary. So if your salary is \$36,000, you would place 3 paperclips in the 10,000 box and 6 in the 1,000 box. Since no one knows who put which paperclips in each box, you can add up the paperclips and average them.

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Each person adds a random number to their salary (the random number can be positive or negative).

The first person gives his sum to the second. The second adds the 2 sums together, and gives it to the third. The third adds the 2 sums together, and gives it to the first. Now they each subtract their random number from the sum, passing the new sum to the next person, finally arriving at the true total. Then they can take the average.

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