## Solution to Puzzle #19: Find the Average Salary

This puzzle generated more responses than any of the other puzzles I have sent to date – thanks for the overwhelming response. What was more heartening was the creativity of the different solutions I received. In the solution, therefore, I will try to describe as many of the solutions as possible. Before, I do that, I first need to give credit to Gurmeet’s blog (http://gurmeet.net/puzzles/) where I took the puzzle from – he has mentioned that a friend of his asked him this puzzle in 1996.

The simplest solution is the following: One person takes a large random number, adds his salary to it, passes on to the next person who adds his salary to the resulting number and the round goes on. When it comes back to the first person, he subtracts the random large number and gets the addition of all the four numbers and divides it by four to find the average. KJ was the first one to give the correct answer on the blog.

Similar solutions were sent by other folks – Rajwinder gave a small variation to this puzzle – wherein each person adds a random number in the first cycle and then subtracts that random number in the second cycle, thus arriving at the same answer.

Found another variation on Gurmeet’s blog site where I took the puzzle from:

Each engineer can break his salary in two parts(need not be equal) and whisper into both left and right neighbor’s ears. Then Each engineer will add the salary of his neighbor’s and announce it. They will add the total and divide by 4 to get the average. This way no one will be able to find the average of other three.

Tarun Gugnani gave a variation of the above by dividing into 3 parts instead of 2 and whispering the three parts to each of the three people and then doing the same.

Alok Mittal gave another interesting answer, though people end of revealing a very small part of their salary in this process:

this has been a real tease… does this work (though it does communicate more than an iota) – each of the engineers takes responsibility of totaling a certain “position of digit”, i.e. units, tens, hundreds etc – for a given position, the other engineers tell the totaler their numbers. So everyone knows some digits of the other people’s salaries but no one knows anyone else’s salaries… of course, one can use binary notation to make number of digits larger than what the decimal notation would provide…

Finally, I got another very interesting answer from Rajat Bhargava, whose answer is complicated, but very unique. It is a bit difficult for me to replicate here and hence attaching the answer directly. number 19

Thanks to everyone who tried – hope that you all will repeat this for the next puzzle which I think is even more interesting.

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