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The total cost of salaries in a company

Puzzling Asked on December 22, 2020

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

12 Answers

Here's my solution:

Correct answer by F1Krazy on December 22, 2020

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

Answered by LogicianWithAHat on December 22, 2020

Edit: If there is only one try.

Answered by Jan Ivan on December 22, 2020

My comment turned into an answer:

Why is it different/superior ?

Why is in inferior ?

Is it a valid answer?

Answered by BmyGuest on December 22, 2020

The following works:

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

Answered by Gareth McCaughan on December 22, 2020

This is how i would actually do it practically:

Optimization:

Answered by Falco on December 22, 2020

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

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

Reality check:

Answered by Peregrine Rook on December 22, 2020

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.

Answered by Scott on December 22, 2020

Answered by Nautilus on December 22, 2020

Slightly similar to some of the answers.

Answered by five6 on December 22, 2020

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,

Answered by toto on December 22, 2020

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