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

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.

• Well, Robert doesn't earn $3300$ (since he does not work for Blue), nor does he earn $3700$, so he must earn $3400$. Can you finish from there? – lulu Apr 3 '18 at 21:47
• For your reference, these are called logic puzzles, and the typical way to solve them involves making (in this case) three tables of size $3 \times 3$ (rather than your two tables of size $3 \times 3$), and using the clues to mark the table. If you Google "logic puzzle" there are other examples where you can practice. – angryavian Apr 3 '18 at 21:50
• @lulu That's exactly why I mentioned the necessity of more than just words but a graphic as I'm not good with deduction. In other words, is this consistent with the table I built up?. As the other possible choices are Audrey with $3300$ or $3700$ and Allison with the same possibilities, but in the clues it does not mention anything from their salaries explicitly. – Chris Steinbeck Bell Apr 3 '18 at 21:51
• I don't see a graphical way to proceed. Doesn't mean there isn't one, of course. My approach is just to look for any deductions I can make and take it from there. – lulu Apr 3 '18 at 21:53
• @angryavian Thanks for that. I'll take a further look into that. But from this problem is my approach reasonable or is there anything inconsistent?. – Chris Steinbeck Bell Apr 3 '18 at 21:53

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.

• Thanks for doing a grid it helps a lot. However I noticed there is something which doesn't seem to fit. In the problem mentions that whom does earn $\$3300$works at Blue technologies, so this square should be marked with a check sign. From then all the rest doesn't make sense. Can you please check this up?. Although the answer seem to be okay. I'm a bit confused as it looks that Audrey could work for Blue technologies and earn$\$3300$ and Allison to be the one who does earn $\$3700$and work for Electric tomorrow. Isn't that so? By the way which software you used to draw those grids? – Chris Steinbeck Bell Apr 4 '18 at 18:44 • @ChrisSteinbeckBell Thanks for checking! Corrected above. In fact the lack of any impact there highlights that we didn't need the second given fact at all - all we need to establish is that Robert doesn't work for Electric, and then it must be Audrey working there. – Joffan Apr 4 '18 at 19:11 • And I just used Powerpoint to make these grids, like most of the other graphics I've used answering MSE questions. – Joffan Apr 4 '18 at 19:12 • Thanks for correcting those grids but there is something which has left me pondering for hours. Wouldn't it be also plausible for the opposite relationship be true. I mean Audrey could earn those$\$3300$ and work at Blue tech and Allison be the one who does work for Electric tomorrow and earn the $\$3700$. Am I wrong or is this choice contrary to what has been stated?. – Chris Steinbeck Bell Apr 4 '18 at 19:19 • @ChrisSteinbeckBell - One of the first (additional) positive facts we establish is that Electric pays$\$3700$. If Audrey earned $\$3300$, who would work at Electric? The very first fact given is that Allison does not work at Electric, and we also have that Robert doesn't get$\$3700$. – Joffan Apr 4 '18 at 19:32

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}

• I really tried hard to follow this method but it doesn't help me much. Nor does it mean that seems to validate my "answer" but i feel that this sentence "by process of elimination" does seem to magically explain like this, okay um... the answer is this. I guess you meant that by elimination is using the fact that for one company there is only one salary and let assign names at the end of solution rather than the beginning. Is this a recommendation?. Generally speaking in this puzzles from where should I begin?. – Chris Steinbeck Bell Apr 3 '18 at 22:21
• thanks for clearing up of what was written but for some reason this way is not very digest-able if you know what I mean. What does the vertical pipe represents? A division a slash I'm confused. I don't know if it would be advisable to use this method at an exam as it looks very tedious to write down everything individually but scrapping that commentary I'm curious. Wouldn't it be also possible for that Allison to work at Electric tomorrow and earn $\$3700$and for Audrey to work at Blue technologies and earn$\$3300$. Is that a valid possibility? Can you check that?. – Chris Steinbeck Bell Apr 4 '18 at 18:48