Three co-workers would like to know their average salary. They trust each other to be honest, however they do not want to disclose their actual salaries to anyone else.
Determine a strategy so that they can find the average.
First number the three people, #1, #2 and #3. Let the salary of person \(i\) be \(s_i\). Also, make each person come up with a random number \(r_i\).
Then use the following strategy:
- #1 writes the value \((s_1 + r_1)\) on a piece of paper and hands it to #2.
- #2 adds the value \((s_2 + r_2)\) to the value they see on the paper that #1 gave. They write this new value \((s_1 + s_2 + r_1 + r_2)\) on a new piece of paper and hand it to #3.
- #3 adds the value \((s_3 + r_3)\) to the value they see on the paper that #2 gave. They write this new value \((s_1 + s_2 + s_3 + r_1 + r_2 + r_3)\) on a new piece of paper and hand it to #1.
- #1 subtracts \(r_1\) from the value they see on the paper that #3 gave. They write this new value \((s_1 + s_2 + s_3 + r_2 + r_3)\) on a new piece of paper and hand it to #2.
- #2 subtracts \(r_2\) from the value they see on the paper that #1 gave.= They write this new value \((s_1 + s_2 + s_3 + r_3)\) on a new piece of paper and hands it to #3.
- #3 subtracts \(r_3\) from the value he sees on the paper that #2 gave. They then divide the result by 3 to obtain the average \(\frac{s_1 + s_2 + s_3}{3}\), which they tell everyone.