What is the best way to solve a puzzle involving sets of information which seem in disorder?

Question

The problem is as follows:

Allison, Robert and Audrey work in three different companies named Silicon creative, Electric tomorrow and Blue technologies but not necessarily in that order. Each of them works for only one company and their salaries are $\textrm{3700 USD}$, $\textrm{3400 USD}$ and $\textrm{3300 USD}$ but not necessarily in that order. If all we know is:

Allison does not work for Electric tomorrow

Robert does not work for Blue technologies

Whom does work for Electric tomorrow does not earn $\textrm{3400 USD}$

Whom does work for Blue technologies earns $\textrm{3300 USD}$

Robert does not earn $\textrm{3700 USD}$

Where does Audrey work and how much does she earn?

The alternatives given are:

1. Silicon creative, earns $\textrm{3700 USD}$
2. Silicon creative, earns $\textrm{3400 USD}$
3. Silicon creative, earns $\textrm{3300 USD}$
4. Blue technologies, earns $\textrm{3700 USD}$
5. Electric tomorrow, earns $\textrm{3700 USD}$

This puzzle has left me in doubt as I don't know where to begin. Is there any method or algorithm which can led to find the right answer without getting tangled up with different sets of information?

I've been advised to build up a table: which I did and is shown below: However I'm not happy with it as it was some kind of tedious to build up and I'm not sure if it is right.

From this method I concluded Audrey would work for Electric tomorrow and earn $\textrm{3700 USD}$.

But again, I don't know if this way of filling a table is the best way to go with these kinds of problems. Maybe if this is the best approach then which arrangement is the recommended? I must sya that what it would help me a lot isn't a straight answer but rather a detailed step by step solution on what to do?. Is there any advise on how to solve this faster and less prone with errors of understanding?

Please do not just use only words I know it can help but it is not what i'm looking for, but rather a graphical or more explicit way to explain a solution for this puzzle.

Answer 1

Okay weird notation.

ALLISON = {ELECTRIC, BLUE, SILICON; 3300, 3400, 3700} are the possibilities for Allison.

ROBERT = {ELECTRIC, BLUE, SILICON; 3300, 3400, 3700}

AUDREY = {ELECTRIC, BLUE, SILICON; 3300, 3400, 3700}

ELECTRIC = {ALLISON,ROBERT, AUDREY; 3300, 3400, 3700}

BLUE = {ALLISON,ROBERT, AUDREY; 3300, 3400, 3700}

SILCON = {ALLISON,ROBERT, AUDREY; 3300, 3400, 3700}

3300 = {ALLISON,ROBERT, AUDREY;ELECTRIC, BLUE, SILICON}

3400 = {ALLISON,ROBERT, AUDREY;ELECTRIC, BLUE, SILICON}

3700 = {ALLISON,ROBERT, AUDREY;ELECTRIC, BLUE, SILICON}.

So let's go through the clues:

--Allison does not work for Electric tomorrow

So:

ALLISON = {BLUE, SILICON; 3300, 3400, 3700}

ROBERT = {ELECTRIC, BLUE, SILICON; 3300, 3400, 3700}

AUDREY = {ELECTRIC, BLUE, SILICON; 3300, 3400, 3700}

ELECTRIC = {ROBERT, AUDREY; 3300, 3400, 3700}

BLUE = {ALLISON,ROBERT, AUDREY; 3300, 3400, 3700}

SILCON = {ALLISON,ROBERT, AUDREY; 3300, 3400, 3700}

3300 = {ALLISON,ROBERT, AUDREY;ELECTRIC, BLUE, SILICON}

3400 = {ALLISON,ROBERT, AUDREY;ELECTRIC, BLUE, SILICON}

3700 = {ALLISON,ROBERT, AUDREY;ELECTRIC, BLUE, SILICON}.

--Robert does not work for Blue technologies

ALLISON = {BLUE, SILICON; 3300, 3400, 3700}

ROBERT = {ELECTRIC, SILICON; 3300, 3400, 3700}

AUDREY = {ELECTRIC, BLUE, SILICON; 3300, 3400, 3700}

ELECTRIC = {ROBERT, AUDREY; 3300, 3400, 3700}

BLUE = {ALLISON, AUDREY; 3300, 3400, 3700}

SILCON = {ALLISON,ROBERT, AUDREY; 3300, 3400, 3700}

3300 = {ALLISON,ROBERT, AUDREY;ELECTRIC, BLUE, SILICON}

3400 = {ALLISON,ROBERT, AUDREY;ELECTRIC, BLUE, SILICON}

3700 = {ALLISON,ROBERT, AUDREY;ELECTRIC, BLUE, SILICON}.

--Whom does work for Electric tomorrow does not earn 3400 USD

ALLISON = {BLUE, SILICON; 3300, 3400, 3700}

ROBERT = {ELECTRIC, SILICON; 3300, 3400, 3700}

AUDREY = {ELECTRIC, BLUE, SILICON; 3300, 3400, 3700}

ELECTRIC = {ROBERT, AUDREY; 3300, 3700}

BLUE = {ALLISON, AUDREY; 3300, 3400, 3700}

SILCON = {ALLISON,ROBERT, AUDREY; 3300, 3400, 3700}

3300 = {ALLISON,ROBERT, AUDREY;ELECTRIC, BLUE, SILICON}

3400 = {ALLISON,ROBERT, AUDREY; BLUE, SILICON}

3700 = {ALLISON,ROBERT, AUDREY;ELECTRIC, BLUE, SILICON}.

--Whom does work for Blue technologies earns 3300 USD

ALLISON = {BLUE|3300, SILICON; 3300|BLUE, 3400, 3700}

ROBERT = {ELECTRIC, SILICON; 3400, 3700}

AUDREY = {ELECTRIC, BLUE|3300, SILICON; 3300|BLUE, 3400, 3700}

ELECTRIC = {ROBERT, AUDREY; 3700}

This is a certainty ELECTRIC = 3700 so:

ALLISON = {BLUE|3300, SILICON; 3300|BLUE, 3400}

ROBERT = {ELECTRIC|3700, SILICON; 3400, 3700|ELECTRIC}

AUDREY = {ELECTRIC|3700, BLUE|3300, SILICON; 3300|BLUE, 3400, 3700|ELECTRIC}

ELECTRIC = {ROBERT, AUDREY; 3700}

BLUE = {ALLISON, AUDREY; 3300}

SILCON = {ALLISON,ROBERT, AUDREY; 3400}

This is a certainty SILICON = 3400 so:

ALLISON = {BLUE|3300, SILICON|3400}

ROBERT = {ELECTRIC|3700, SILICON|3400}

AUDREY = {ELECTRIC|3700, BLUE|3300, SILICON|3400}

ELECTRIC|3700 = {ROBERT, AUDREY}

BLUE|3300 = {ALLISON, AUDREY}

SILCON|3400 = {ALLISON,ROBERT, AUDREY}

That reduces things a lot

--Robert does not earn 3700 USD

So

ALLISON = {BLUE|3300, SILICON|3400}

ROBERT = {SILICON|3400}

So this is a certainty:

ALLISON = {BLUE|3300}

Also a certainty

AUDREY = {ELECTRIC|3700}

ELECTRIC|3700 = { AUDREY}

BLUE|3300 = {ALLISON}

SILCON|3400 = {ROBERT}

Answer 2

Well, as mentioned, a logic grid helps some people to organize this kind of problem.

The basic facts given can be laid in a grid as follows:

Then we can use the exclusive nature of each attribute to exclude other possible earnings at Blue and other places paying $\$3300$:

Then the salaries at each company can be inferred from the lack of other options:

Then a slightly less obvious inference - the salary of $\$3700$ at Electric allows us to know that Robert doesn't work there. On the grid, the checkmark at Electric/$\$3700$ "sees" the cross at Robert/$\$3700$ around the corner and can echo it along the other direction.

And finally the lack of other options shows that Audrey works at Electric and again the checkmark can be propagated to salary from the round-the-corner alignment, giving the answer. Clearly all the other checkmarks can be completed also at this stage if desired.