Wednesday, May 7, 2014

Average salary of n people in the room

Question:
How can n people know the average of their salaries without disclosing their own salaries to each other?


Solution:
Let's say salaries of n people (P1, P2, P3.....Pn) are S1, S2, S3.....Sn respectively. To know the average of the salary i.e. (S1 + S2 + S3 + ..... + Sn) / n, they will follow the following steps -

  1. P1 adds a random amount, say R1 to his own salary and gives that to P2 (P2 won't be able to know P1's salary as he has added a random amount known to him only). In this case, P2 will receive the figure (S1 + R1) from P1.
  2. P2 does the same and gives the final amount to P3 (without showing that to anyone). Now P3 will get the figure (S1 + R1 + S2 + R2).
  3. Rest of the persons (P3, P4, P5.....Pn) do the same. Pn will give the final amount to P1. Now P1 will have (S1 + R1 + S2 + R2 + S3 + R3 + ...... + Sn + Rn).
  4. Now P1 subtracts his random amount (R1) and gives the final figure to P2 (without showing that to anyone). B will now receive the figure (S1 + R1 + S2 + R2 + S3 + R3 + .... Sn  + Rn) - R1 = (S1 + S2 + R2 + S3 + R3 + ...... + Sn + Rn).
  5. P2 subtracts his random amount (R2) and gives the final figure to P3 (without showing it to anyone). P3 will receive the amount (S1 + S2 + S3 + R3 + ..... Sn + Rn).
  6. In the same way every person remaining except (Pn) will subtract their random amount and give it to the next one. Now Pn will have (S1 + S2 + S3 + ..... Sn + Rn).
  7. Now Pn subtracts his random amount (Sn) and then the figure becomes (S1 + S2 + S3 + .... + Sn). Pn will divide this amount by n and get the average i.e. (S1 + S2 + S3 + ..... + Sn) / n and show to every one in the room.

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