Logic Puzzles

10. Three Coworkers Would Like to Know Their Average Salary

Three coworkers would like to know their average salary. how can they do it, without disclosing their own salaries?

Submitted by tartle · Added 7 December 2007

Solution:

Person A writes a number that is her salary plus a random amount (AS + AR) and hands it to B, without showing C. B then adds his salary plus a random amount (BS + BR) and passes it to C (at each step, they write on a new paper and don't show the 3rd person). C adds CS + CR and passes it to A. Now A subtracts her random number (AR) and passes it to B. B and C each subtract their random number and pass. After C is done, he shows the result and they divide by 3.

As has been noted already, there's no way to liar-proof the scheme.

It's also worth noting that once they know the average, any of the three knows the sum of the other 2 salaries.

Solution contributed by Jeebok.


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Comments (5)

aggynd 1 March 2008

ask each coworker total of other two's salary. total the three figures and divide by two.

Jeebok 30 March 2008

Person A writes a number that is her salary plus a random amount (AS + AR) and hands it to B, without showing C. B then adds his salary plus a random amount (BS + BR) and passes to C (at each step, they write on a new paper and don't show the 3rd person). C adds CS + CR and passes to A. Now A subtracts her random number (AR), passes to B. B and C each subtract their random number and pass. After C is done, he shows the result and they divide by 3.

As has been noted already, there's no way to liar-proof the scheme.

It's also worth noting that once they know the average, any of the three knows the sum of the other 2 salaries.

dedo 3 May 2008

Jeebok, you got it!

yuk 28 May 2014

There's only need for the first person to add some number X, only known to him to his salary. Then B would get (X + A), C would get (X + A + B), and A would get (X+A+B+C), will subtract X and calculate the average.

Satyajit Chakrabartty 24 June 2014

Each one of the co-worker puts his salary in a box provided with a lock and only an opening small enough for currency notes to be put in. Each worker puts his salary in privacy. At the end, the amount in the box is totaled and divided by three to know the average salary.

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