The total cost of salaries in a company

Question

Story Version (scroll for TL;DR)
It's the end of the first quarter of 2017.
This means it's the end of the 2016 fiscal year (at least in my country it is).
It's time to draw the line.
So the CEO did his calculations and said we did a good job so we should get a bonus.
Yippeee...
But there is a catch.  Or two.
The CEO values smart people more than hard working people.
So here is his bonus scheme straight from the CEO's mouth.

You all know your own monthly salary but not those of your colleagues.
If you can guess how much it costs me to pay all of you in one month you get a bonus. Otherwise I'll just take you out for beers, but no bonus.
You cannot ask the financial department. And you cannot find out how much the other people make a month.

Now what strategy should we apply in order to know the total sum of the salaries per month?
I really want the bonus.
All I can tell you is that we are at least 3 employees and you can ignore the tax calculations.
Note: This is just a story. It didn't actually happen... because there are no bonuses.
TL;DR
Each of N people know a number but don't know the number the others know.
How can the people find the sum of those numbers without finding out each other number? N >= 3

F1Krazy · Accepted Answer

Here's my solution:

LogicianWithAHat · Answer

Assuming everyone gets to hear every guess, and that only one person needs to be correct for everyone to get a bonus:

Jan Ivan · Answer

Edit: If there is only one try.

BmyGuest · Answer

My comment turned into an answer:

Why is it different/superior ?

Why is in inferior ?

Is it a valid answer?

Gareth McCaughan · Answer

The following works:

[EDITED to add: Be it known that F1Krazy's near-identical solution was posted just before, not just after, this one.]

Falco · Answer

This is how i would actually do it practically:

Optimization:

john · Answer

Just get a random person to hear and add the totals, then report the total to everyone. No one is the wiser regarding salaries and everyone gets the bonus. No computers involved. Keep It Simple Stupid.

Answered by john on December 22, 2020

Peregrine Rook · Answer

This is somewhat of a muddle of BmyGuest’s answer
and the F1Krazy/Gareth McCaughan answer:

Reality check:

Scott · Answer

Assuming you're in no huge rush.

Have everyone get together and state their number, get someone good at maths to add it up.

But first, to anonymise it:

To keep people from getting some information,

Keep repeating this process for a sufficient amount of time.

This is similar to other 'random number generator' proposals above, but it mitigates one flaw I see with these. To explain this, name a color and a tool.

Nautilus · Answer

five6 · Answer

Slightly similar to some of the answers.

toto · Answer

Take a small bag, everyone has to put 2 papers in it :

So let's say

Once everyone added their 2 papers in the bag,

The total cost of salaries in a company

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